{"label":"83.6.a","level":83,"weight":6,"dims":{"new":34,"cusp":34,"eisenstein":2,"modsym":70},"old":[],"T":[[2,1],[3,1]],"status":"proven","checks":["dim M^+ at levels [1, 83]: [1, 36] (certified at ell = 2147483323)","T = [(2, 1), (3, 1)]; h of degree 34 = 1 x 34 (phi(ord eps) x dim S_k^new); 7 primes, 0 rejected"],"newforms":[{"label":"83.6.a.a","letter":"a","dim":14,"charpoly":["1206108837762336","-1168728914301808","236655664683472","16266519583240","-7712884204560","152523286405","88586418009","-3675520827","-479646070","21384849","1322678","-45889","-1866","30","1"],"traces":["14","-13","-17","133","-162","-15","-247","-609","679","-519","-413","-1193","-2942","-1176","-1990","437","69","-4532","-2446","-6353","-11006","-13799","-7823","-22851","-9548","-12643","-19286","-19476","-5449","-16388","-9055","-10081","-12290","-15034","-8990","-9464","-46585","21469","-4304","3839","12585","36275","-27158","81915","-23282","8541","-12288","105743","35285","122046","27796","11795","-77086","170469","10248","119410","-25034","4917","64705","144740","-33501","130998","10223","73789","74132","88985","-125486","157106","77860","131976","57934","189948","-116530","173369","108657","49111","-67514","167126","-17628","99483","25726","187361","-96446","195193","-262070","125125","-291809","-399591","-188766","136339","-291368","-278885","-476138","-34406","-346660","-47651","-351786","119329","-708674","-459898","-511176","1813","-572748","402915","-210764","-307763","70550","-307925","-262363","231990","-257910","-592208","-230705","558826","-420356","229563","-544372","-60925","-333179","522416","172175","430753","-36686","-473434","20100","-211827","-503843","-652417","-55966","21458","531067","827247","-825798","1010457","306236","-300224","-68392","486838","-296754","719744","-933508","296606","651122","-100624","-402810","685462","1041758","118267","-564544","929699","125969","718463","1326023","807733","1169146","385290","-1507126","-365860","174830","311399","1375548","-306713","-1110544","1064995","1315368","89557","1370909","1304807","471420","720111","2556514","-1503801","370363","1707547","12615","2119795","363934","791832","1564902","1069821","96014","1472187","1623039","882287","1218292","893589","-1133750","-530042","-1441070","-2060672","2036773","339207","-2732305","-90714","2118556","-3266613","-1209023","-489640","572081","427248","-1112550","-3706738","2387770","-212257","-2341818","613808","2479179","-4897985","-1159252","-491680","-699060","-2487165","-811256","-4990767","2772920","145125","-2535950","1391187","2579732","-4750774","-1913010","-3117393","-2050658","-1549862","-3064557","-2011240","3086384","-2411378","-2743375","-1391547","6080584","-5207003","-1192068","-682917","235412","1841345","2093522","-5286911","-110290","-2033724","-2732681","-5292788","-319025","-5561065","534092","-2221334","-1133880","4610260","117113","-4927084","2393014","-957189","-7229812","-1662146","1678772","493189","346918","-1739122","559720","758702","2027765","-2118854","2752450","1061561","-609712","-648371","1859492","-4280981","1379538","84346","1903998","2428686","3900148","638056","3656797","2403106","-4430073","-5329351","8950938","-1036060","6208902","3507116","5974676","-3316102","984712","6361828","3634934","4837644","-683155","3660246","9155560","-3396310","2654251","2625974","1656466","3579757","-252422","-1660525","3837598","362669","2909542","5713256","2401184","-4835877","2925574","4931443","-2900912","-1556793","8516978","2331163","3754420","12021822","-4716621","314117","8878092","7197692","-5521635","8322810","6653108","3033259","6743948","-2389420","7538458","-9442919","-1167138","6911265","487196","2044635","-71400","1670282","5428752","-916237","-2463032","2736349","7104368","4760081","-317150","-9988706","11245573","2007601","-6210673","-10561845","1329934","3010235","-5459058","-1074467","-10545016","4113777","-7986539","-2405477","12367762","-15967687","-937129","-6123357","-1399304","-7120872","-20601281","139437","-6575711","1405145","-4490900","6848370","6082545","906481","-8279212","1163919","3337702","-4602985","-21229619","3538440","10856854","-17220365","-18093309","-9697825","-4088592","22366374","-15547672","-2174143","-15856708","-4461120","-3523189","182837","2316491","-7144547","-9741334","13495959","-11881210","9272178","-9616478","-1754046","3084712","-1664981","-8160336","4589291","2284672","9213936","-12065285","-5332431","-11834254","-9795846","-3714515","3416384","-5476082","-5246382","-14555612","15329369","-4042617","-24474723","-9246041","-6386304","13989302","-13650216","-16303487","-3334087","1116018","29066971","-21095274","9908808","-4486425","-5676296","-19150032","2992616","11641098","11589291","-10932265","20702242","-54098","3486475","-33076298","12934039","7810941","-3590725","-5634746","-8708511","4523420","21279169","-10391048","-3801392","-8818482","8550590","4586410","24393042","-934755","-2544815","-1407224","4398016","4868904","21280424","-11753178","-3268643","24853430","7732548","335307","-8475334","4187904","40258","-13422944","-1742222","2085988","32708711","-3523410","-16470859","-1522633","930035","16085224","22955538","10700320","15636365","-5105120","5105084","19775192","2354771","-3915728","-19581598","16259596","21352735","-12721490","25205044","10836185","10737024","8737542","15314762","-7262113","28713368","-5533440","29230014","-5387426","3073017","-9047420","18932934","1553840","-24331698","-7031276","953047","27190050","14096578","-15184054","103335","3531371","5615260","-9146229","-2698773","-17005852","10786235","14745232","38002464","4314653","17366410","10140697","-4566254","32197818","-11304129","-16660730","20695518","24374060","13660426","-15462954","-8587825","38696410","4654814","10382175","-44195534","25173989","-3626946","9251118","42084716","-20933014","15958439","-2571489","19965550","8888691","16055995","-2673318","-5179344","32916900","7161195","-24251108","-26225225","-24640551","2287406","-13927646","-30078610","15453610","-15268872","-12081594","-11377040","18717657","-9238680","-33505683","47651133","25956866","-27909006","-13723250","-43598668","-4208456","64164171","-4245476","-33536657","-821396","-9416960","6982050","3766762","-9500027","-52403860","-5805622","-61781110","24515768","4928974","-35855052","-20126618","26087564","-60672532","-35523894","-6956483","-5539537","-8729856","3641780","-22032961","-8657618","-8920462","1701583","-51643428","11109336","-27812598","18875196","33078190","-30513542","-43733498","-330184","-44654646","18084952","16120387","12279805","-54609097","25778744","-15854411","-44243316","13808096","-12581446","34394583","-3131510","-34325754","-39264850","-54808784","-27314784","21002522","21401375","-14444025","13110738","-3171090","43028524","-42810551","-3196224","22560923","14231854","28873365","-7628733","-41071760","3042015","-639711","-16865897","-38445166","11555620","-85271262","11898934","-9115766","-10718782","-18652805","9389140","9982306","21002354","-82102600","41483134","57360383","29239378","-21820978","-33530738","-37203677","11137734","36086391","27179890","-40960986","1765102","-18239344","15608564","35279164","-17515270","44087091","15473366","-25288670","29330372","-51164445","12945574","-54489187","26524342","-21095377","805346","7679510","-2890220","-39498834","-23910264","-91001833","20756192","4195401","84904854","49723934","-30478856","-9060989","21950812","24104429","23505572","-13488217","-3154805","-19429394","44124714","66055094","8222284","-67735479","-24939376","-15198039","69194172","22119195","-3241550","-20021831","20311140","-21822037","-23427378","-25986229","70502566","3945456","74330813","-11753225","21928111","40851505","51714508","35159527","-42153474","367273","37714780","58762905","36298173","-104150218","19417168","39846187","77658060","19550744","15869132","26574057","3504184","32351178","16464808","45687248","35483206","37415541","-36318512","83484495","42036892","65592768","-14355584","-43247615","29045090","27949264","-42742394","30668038","26598505","54684236","8282303","14989457","122299153","-14607074","31510256","7260349","6993137","-72271112","-10081454","58610983","38533644","52646579","43892707","8182960","32754424","33869583","30375098","-58713911","30177694","94452211","-4677631","97554109","-11820948","44968442","8458852","-82272922","30024458","76760994","1191296","73390471","-52494627","-52590005","-17904999","25935256","13563944","-91519549","-81546949","51764199","-70488808","111929124","-28617642","79230431","-37223374","-78782248","-49527086","-65747819","32906372","46852593","-33185141","-98790254","72674430","33035859","-73129670","5802262","-7585432","2143129","-113919083","8048919","42083390","-24521604","-40889733","-55867047","74837642","-16341554","25235710","5569724","-53534176","-61139462","39089748","92409399","-23035376","-38378824","-89436444","1086840","54238886","-78274007","-71537172","-72331224","-11942974","-26769406","-55296432","20570342","72722722","10707217","-100635968","-11987085","-113266318","-95651673","-7189780","99719255","-79116184","17313830","-67365504","-65172056","80230292","-100322030","-82502528","-84661080","-22254406","23339027","-51028314","-70302229","-32119438","3575391","27352478","-187168961","50672797","-14384572","-147110114","46454544","-102112886","144787863","-61907629","10225956","-25184465","-79706150","8622442","-44434168","19300942","-110288082","-130291538","-76685993","51208586","31389262","-16559332","-103868066","-115304753","-68279035","-43364788","-162003861","71205699","232812530","-128346315","7399425","192173105","-16512900","-42256879","123511669","-54158684","28112706","82328392","-24173333","-287540","-82635510","14588108","140514631","-9803122","-12967294","30807478","96672792","-205170510","118293284","-2155218","105334882","13666365","72546519","-97917868","-179419914","-763988","76386391","-35382022","74734303","-21644496","-54522562","-134730620","-9328048","4841860","60903758","-98949296","27274874","70708748","33383468","20833620","-37838605","-117974132","-21228204","-66745738","2651974","-75915328","105002473","-69713219","144192678","22566514","-31576013","65337671","-20932394","2845157","36538572","1724784","113626126","49475528","153486721","-154055692","42219563","114368786","50407441","41916124","-61202757","-107321379","36781230","-83907588","-102890587","112357233","88170610","-130362584","63855750","-48311886","-115211301","66552006","-142797495","-107095820","108987216","-144193188","44894604","165790157","-26598580","-85696729","141746521","224358490","92529628","-39559602","97210598","-123857760","146911152","-34329380","162094009","129035863","-72430345","19777278","127546300","208049453","69560276","-1288980","-70951308","50093781","189061076","118516400","-38642306","90301926","153457770","-169678072","-289890372","84466630","101626124","100269576","148324390","-117602810","67583122","-88718896","63999839","217371073","209444950","-211064232","87920546","-50001725","-49221503","-111144200","111774706","118150354","-129318031","205190586","-33884047","-3365128","87874328","-59046311","164536396","-41600828","-26457040","-53776562","8218577","101758681","69766349","250599726","65457476"],"derived":{"al":[[83,1]],"fricke":1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"83.6.a.b","letter":"b","dim":20,"charpoly":["24826081189085403897680","52924821601381361181808","-27466260911857785565328","-10241142817009646582134","742441695991257810002","269978724552071367110","-9289698811777097141","-3099869138360500064","71975712093366637","19333515828475298","-376148208590796","-71055482224630","1321448502777","157725819186","-3004775505","-207251872","4167415","147918","-3166","-44","1"],"traces":["20","7","37","373","88","129","439","351","2137","481","313","1399","2804","0","1610","8885","2381","3568","2608","1647","5881","18703","14802","34687","21858","20301","17005","27472","19515","22256","13135","23009","17539","-8340","-6310","20812","45999","-587","-13794","-18769","-4772","-87449","16018","-87813","74","8347","-9788","-40281","66263","-127676","-26081","-5633","21376","-248923","-30582","-169014","-24834","-39633","40943","-225482","27191","-213850","-40384","59353","-27308","-287573","64688","-270638","-63560","-109632","63938","-217532","65234","-428799","-18321","-158945","-183287","-237334","-64074","-201521","165012","-129233","137780","-512695","490786","2881","479693","493355","-88378","-123605","648104","385779","490497","-87006","225060","800961","312918","565425","617014","-169410","552084","-343637","620772","-302265","565178","100893","377804","533947","719145","-343514","513843","510804","377287","-725786","618302","674211","795554","119345","-3005","133768","1002481","-470505","507490","-149314","505692","-1536801","512599","-474705","-423820","51938","-28170","17851","886162","67529","-75946","-201726","548500","-450222","-363452","-1436686","-599932","-134494","-350418","-920608","108230","-1269890","-289558","1940571","-517898","-2074513","623339","-937305","-226268","213641","-1450392","-1967628","656320","-1506912","-1999418","-1185197","-468628","-1086065","-871328","-1650293","661602","48223","-909745","-3078901","1095962","-1447977","-1694986","-445443","-63629","-1207463","-992935","-4079085","-280859","408928","343900","-2367881","118844","-936781","-5073599","1110825","-1620742","-3304125","-643753","-144060","-140049","3678872","-2638985","-859413","2897248","719642","-3625512","7892235","645833","4771056","1219854","390970","-1869090","3018294","1026493","600911","3803264","2596680","2059458","6735087","-1789702","5696160","-2053276","2380809","812330","7357653","-2437128","-287033","3549847","2630831","-2131836","6058540","-386226","4484023","1935652","-4398068","-1503059","10900944","-6135856","3673168","5025038","-337559","-8012683","4561949","224176","2974623","2743956","7272089","583078","6300161","-3109644","-2348042","-966637","1015632","-897238","2765107","-4062338","-6549802","2247380","1282576","254893","8036692","-4842882","1719995","3632476","-55748","-8440282","9695749","-351636","-2583246","-72955","-2827706","4249374","5848082","-9190374","-2791403","4602740","1010173","-6571476","9559141","-456432","413462","-2219960","-6867170","-2466594","4073292","-6637093","-5968630","7573350","-3633387","-2090774","975416","-3926958","6759716","-2751478","464206","-7014940","4723140","-2223326","-3804896","4206259","-3995890","-10851724","1855328","2719702","2022388","-8591434","-10970839","-1225751","1824835","-2555504","-4875083","6108816","5353362","-5115738","-11196693","1291482","-12655635","-2274510","-18691685","3690380","-68137","-14701108","3491058","-2545769","-1698435","-18203100","-2790138","-1307043","-1723382","2312175","-3168553","-5069490","-3880974","-8361806","-3246007","-3156224","-10900763","-8505475","-16853615","-4242532","-9575654","-494092","2569597","13716476","1839733","-10950516","-25470083","11779684","-5440996","-1835393","3075389","5329979","194671","-1412593","7385059","15654056","-20597835","76432","12302553","9827881","6304029","-16111862","3553805","14451135","10525599","3006624","-7660580","30397859","-1541031","1971067","1842689","4024030","7758278","-3338536","20084457","13831524","9444885","38298","16898483","38017198","-5201544","-15978904","7735087","18273259","-1189939","2357356","-9819454","26230006","-16083981","-557230","1080564","5863835","6359339","2265609","34123467","12469958","6996137","-3858446","9061882","13908058","11348930","-16902620","33173721","3054148","-3560785","2027272","718448","19154666","-13782089","28192378","-30115778","20308572","17146436","-12890554","29203282","9735788","-48378633","-7440699","-10936093","15264847","5391172","-5827170","12935556","1878689","18006997","606232","-16181861","34664058","-27676388","-4259223","-5691090","-3544200","23209688","-6834940","-10911645","20519731","8998502","-4128131","4251049","7569134","-34985167","-7406121","8705379","12251650","14434305","-18252374","9870889","3531916","-18669904","-14945812","10124058","16244203","-2610090","-7157125","-508219","21798416","-22238104","10926112","-8585664","22169656","-6254241","-7891614","12102916","16181551","-13738506","-16523868","-53717466","20212096","-22325382","1024093","-27124247","-15228634","-33903211","630369","37470007","17728258","-58121202","19228014","12611739","16722074","-16792920","-17885618","-4051911","13784512","-221994","-5521146","-11304349","33583550","9511768","-2232345","-34581912","-20128118","17207628","-54442446","11092920","22297832","-54284212","9465024","-50580399","8697526","-62069162","-29699124","17353086","-2666833","4191953","-25091824","-91691530","-18903182","888681","7460745","8719008","-16712041","-18269609","-25970340","-72514871","3499716","1556270","-13559709","-60112594","27686377","-470006","4702396","-14965019","-13300818","-9550274","-21829076","-47076770","-3297480","-37109171","3717139","-45566622","-8368808","-5739430","-11390897","26418270","46292395","-58312280","14133289","64147723","1253488","-6342942","-4662368","38389167","19489512","45436600","-3225612","-12271841","-4923522","-28948821","-14884220","21515212","-6552600","54528330","12700382","-8717420","-16969298","-7558728","35717835","100976532","-16439898","-7294161","-30839414","119285286","20834486","76562652","-4761342","-52555001","3956916","16260533","2475784","37577082","-11780593","30957690","5398555","25434374","3417402","7181322","34491017","30219586","-25662668","42880986","-14910142","27627222","11785877","-71809311","687710","33931500","31712392","4239795","-37834814","-24018196","3024271","157727232","33281134","-10754490","-40214080","-92140082","-12691710","115883110","16469758","61334190","-30052215","47914179","22412837","74513727","-36989512","-16701049","21886172","20071164","-7778608","-26902427","-39461040","182534810","5642762","8876792","-39232594","43551214","24437066","100450607","-18932763","-22090178","4501696","37306693","35466418","29901947","5656728","-80386515","26679483","81887264","-8551455","1389893","-52495862","-14207706","-8776700","40260692","-7356760","13224800","-24718054","-50532605","2229023","72052702","-836140","7143684","2989572","-33058057","2202978","-26700798","45016514","84763467","13006340","-92902429","-14254242","107459710","-5915578","34850120","35027060","-11133868","-34607242","44252707","-89313231","60308554","-68522169","-13507961","63017318","30209155","-20946224","-111964873","-16042538","-62888034","-28214672","71694308","1949198","-17677453","-21393942","2418039","-69227074","-34453610","16501008","11137307","-19444024","-69602805","5476931","116228657","10429355","63399878","-31506005","-140637322","-28812050","36206743","-63506872","11088945","-26212908","-39037641","-14771726","-71973129","-3905268","-65571307","-6160842","-104114951","-50141026","-60707188","-32879273","122046127","-8606348","46234833","23531796","30811909","-15074674","87322445","-7896346","-67080839","15498418","25135218","-36700846","-82336653","-155894728","-27973694","-17957442","129838161","47430176","-63337190","-122739352","-52638772","6541690","92407337","-82009624","36145123","40703988","-66805100","-88955840","-33141413","-95113076","55018358","-22469859","-69789176","-26401291","-64311654","12195101","-21614435","-37324670","-27006454","-49287166","-137016659","22281085","61055792","-107739288","-74183903","-63875542","-12417421","-56981230","-63614514","-14561032","-63514601","-7157248","-42636271","-61043286","-48222177","14721793","66409597","-32313846","10231770","23214656","94842684","-147232636","-75514398","-26681600","-45226549","112513609","25066175","-7241734","-39208540","-105055150","-301697","97247365","4856763","-9152600","-3597424","32725222","-73691645","57096318","-59787268","-30983486","140386217","-4809560","76526165","107022625","-77321758","-47109175","73304903","92864730","-44086178","17337466","-32443215","39651383","248272519","-34923810","98169284","29365062","-10370111","69856670","-31188714","9384251","205396812","90293186","-35327094","35885464","-38418445","139411510","-7797952","187265840","71128644","-139935334","-77637241","-83530156","75468292","97276456","41658670","126154394","42971458","-205518326","-1092027","164775932","-36083797","12118112","193895937","19301852","-90236129","44863464","50492852","82199750","-26243100","46607846","-73984910","58855128","103212212","-83697555","-149808423","32138274","30139743","115475352","3313609","18039026","149198223","-20165038","-38297324","224566210","-128041854","55883007","-71660403","16893113","74104736","3182693","-20162602","26627512","-20462718","-47270416","-101175686","233579962","-40665459","60027578","-50380860","68369168","-25585362","54375739","-69322673","67134632","46609431","-97623765","-10936750","140635379","53671841","75629436","57933182","39010751","46131441","-24200546","-53101886","146924476","-38789333","74309658","121728982","93827468","-63000333","-158174270","194584826","134314918","-66494654","136791172","-2219716","115184010","30102628","-100839495","94465869","175342134","-14171852","-237617874","-259616741","-12109752","261409849","-29120823","-119431062","104558431","49747458","-36199412","-10614362","337101940","-112074582","-279520972","110213444","-59794067","-152715737","23617422","129800446","30870252","282451732","-49149668","-247665423","65992847","-201498994","40755222","-179265947","98305345","91687164","2156257","155447000","-61186150","223538642","28612000","-57490567","91432696","-135055317","-33320348","82246805","79846436","-267555245","49116261","-166032618","85468172","17425511","-224434131","90761434","-21240946","121805968","77253196","-57158693","-191935682","-398014675","-49388234","-107855572","-32635123","213694184","60437209","-278389960","72209970","252287621","-132195810","-224565660","183275948","-392724928","79028784","44580472","81965065","180012235","-148441345","103380979","194996962","-149248792","-92570463","14796356","138299094","-181086158","105122127","-122511844","-61432622","-137587670","91125156","-43663556","26914670","-59649492","-392618746","-187329624","-79303020","-79215794","126626330","-108759774","65491814","-146911845","-77616107","99023686","108928156","-329877774","17632374","-91254339","-117277796","-75635698","-63189410","-150460059","231184576","-226324771","-95724376","-400279884","-22731541","-125132534","-290236722","-52927032","48722020","9637711","107645329","-427354727","196497521","221514948"],"derived":{"al":[[83,-1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.249,"computed":"atlas","estimate":{"seconds":0.472,"low":0.288,"high":0.817,"bytes":2077211},"url":"https://sagebrush.space/atlas/mf/83.6.a"}