{"label":"157.4.a","level":157,"weight":4,"dims":{"new":39,"cusp":39,"eisenstein":2,"modsym":80},"old":[],"T":[[2,1],[3,1]],"status":"proven","checks":["dim M^+ at levels [1, 157]: [1, 41] (certified at ell = 2147483053)","T = [(2, 1), (3, 1)]; h of degree 39 = 1 x 39 (phi(ord eps) x dim S_k^new); 6 primes, 0 rejected"],"newforms":[{"label":"157.4.a.a","letter":"a","dim":18,"charpoly":["106339027","815853509","1912138744","258235703","-4693966195","-5299288274","5702758","2306434808","576754029","-262573383","-70946691","9207351","3197723","-38558","-60247","-3064","351","38","1"],"traces":["18","-15","-23","59","-25","-27","-55","-156","107","-8","-173","-141","-108","-99","-210","99","-231","-284","-247","-375","-316","-387","-683","-448","31","-445","-986","-556","-793","-886","22","-1563","-666","6","-1654","178","-374","-1058","-876","198","-358","1332","-422","61","941","3001","-1064","2906","1221","1625","298","1757","-815","2515","-92","2657","1152","2413","-1296","4104","463","479","-619","4316","-1522","7401","-2331","-855","556","4917","376","2721","510","128","-1599","5662","-1488","6374","-801","563","894","3984","-4254","1255","82","1248","444","752","-1395","5926","554","-5955","-838","4639","-5528","576","-1990","-4425","-3577","363","-692","2727","-2073","-1538","2814","3089","-8904","-1960","1336","569","380","-2902","-4721","4590","478","-5903","-3676","1591","-1422","-2585","3661","-3022","-7762","3462","-3534","388","-3452","-11840","64","1954","-4388","-8645","-2628","692","-10480","6273","-8610","-5306","-7324","-13337","1556","-4294","-4776","-8764","1148","-5697","-5505","-1586","-2063","-6324","-5619","-15041","-6891","2157","-9946","-12303","2826","-3694","5503","390","-2506","1721","-6300","-5346","14725","11070","-2598","3680","15798","720","-701","5509","-12","12265","11580","3103","8632","5788","-10270","8234","-1019","-1728","-1970","17780","7450","1682","8956","-9804","26335","-1706","-6649","4759","12885","3903","5960","5288","5170","-9630","3040","5172","25130","-914","-8774","2769","23012","6674","7764","3892","14830","10642","-15050","-9068","16274","7914","-3936","6551","12444","-20860","13602","-5671","2104","-456","-345","16387","20874","-11693","-24330","8365","46318","852","6102","-798","29","3879","706","-16195","9342","-8748","-7348","21602","11856","-8001","-18695","7416","969","-12748","-758","-9123","38998","15161","-4600","-14060","-12802","-10446","4959","29707","9701","-10044","-4476","-34648","-10177","2517","-16610","30487","30680","442","-4916","-15248","349","-16019","-421","-29229","26550","18630","-20791","-10344","3354","21441","17020","2426","-5399","-23259","4961","5426","51361","-22931","-25592","-4653","-1695","-21718","7352","9237","-9013","17283","-3664","-11813","23758","-8385","-6026","-18757","2970","-13912","-14996","32735","-6368","3609","-25740","-14046","8454","-7524","-10810","27011","1941","-2355","-29493","-57046","-1484","-41319","34741","11819","20300","-19634","-46071","-3803","-22614","-20354","28372","15537","30046","-10937","-14785","-42708","16308","-477","-11944","-46200","-18392","-72707","1917","-23946","-6628","-55344","-3824","-12944","-7672","-37297","-51235","-26106","12890","-29591","-4216","-11790","7577","6492","3412","-25524","5815","-44592","-8651","-50000","23655","52652","-20116","31440","-7674","13671","-2347","-63952","55584","-35021","-47004","-30785","-11025","20808","-5520","16475","19746","-50288","-832","20310","36804","14861","-26729","19437","35600","22742","9760","-30463","12280","54895","-11290","40390","-29110","8552","-15989","-13454","25545","63787","5147","-59204","-8270","-18188","-24488","79184","70103","-6163","-18612","19588","-4770","13760","2100","-32714","5434","26309","4652","9988","-24738","38557","39401","20152","-3095","98654","-13356","25891","26605","-43629","-19904","6859","42000","-8746","27892","81888","-13656","56203","-5483","14728","-16724","-10852","25335","102404","35088","-37013","-38496","66911","67417","1647","8254","-33859","26102","60989","-50836","63651","35552","65330","48818","-97795","9077","-58889","10006","20524","27362","-5901","11647","106022","36286","-31438","-18623","-26340","33992","22063","-3611","-1630","-9326","111540","-18199","76675","-13793","22038","28587","-4924","-18010","60429","4449","85500","16518","14127","-1340","52763","70764","14176","-48880","2434","-29220","112218","-46341","-17813","-3434","-87843","-24688","37369","-15796","6116","-977","51492","7438","53641","-31669","-52108","35663","50360","-35678","-90103","-16194","-65358","-8320","-25174","-21730","85730","12640","144296","-3570","-592","-28389","93231","-40842","-41377","-35420","-156303","21133","16255","-20510","-53848","-28928","-19075","-43438","-15982","12172","42575","16510","-87343","-54419","47281","-29150","99875","15088","-168511","-54809","-50991","-9316","-109477","17152","23020","12144","60936","-13004","-120717","-48726","-23245","-28300","37725","-36356","88777","-106990","72314","-44532","-58589","-117201","-106045","-10774","-70612","-54491","143094","-57382","33384","-16179","-37138","-13049","21202","8652","-23777","-14118","-23559","-28006","2230","-30738","-77584","-85300","-33758","-13200","115588","-71712","26524","16425","-16745","-40994","28475","-40614","-42688","-77685","38518","-10597","96965","-158312","6825","-4415","-68054","-37220","-1249","-11086","-64250","-161162","-67295","-29583","60889","-44292","-88202","-5489","-25665","20203","63045","-67792","-1787","-61784","-218282","-9140","81032","-157186","9263","-33038","-3178","-22408","96302","-62062","21489","-9934","-6992","-40424","-96195","30010","34563","74251","38843","19030","124801","924","65010","-3596","8461","15776","122936","-89160","-17283","68590","-79195","41516","-63817","36282","-95676","-50913","14938","-15246","16456","133796","110744","14142","-178095","-19014","-64522","-25837","22736","56582","56578","-31730","174758","-31589","92602","42692","65920","69112","105957","66380","-99544","-21904","123101","-67200","-22971","-86594","49618","10434","6914","71136","45833","21172","63325","120884","57451","-24254","16334","-2794","122961","12623","65298","30960","152388","65716","-40989","-35658","-75445","75436","143966","75215","43004","13188","-40832","25560","-663","-68940","73567","40539","-13330","-4222","-52442","-47136","-111783","-77037","-135465","102406","-97959","115901","-118561","-30914","-5555","31194","84477","228069","152774","-13488","-85533","8883","184844","-2814","11303","-82328","58917","87900","21062","-97432","-25693","71518","-98629","103053","-27568","58374","12858","132547","38848","-23599","101109","238484","-43932","84058","73668","58340","-141615","-42688","-117192","18902","-155859","-16403","86994","-56034","131311","-1332","-72473","176236","73976","100680","-113490","39480","-136399","-64082","66625","235916","-137817","-3925","-150708","-99672","181770","49720","113175","87270","86244","2266","-50884","-39556","-65752","-16256","60494","116202","70287","9551","6460","-22568","120451","119707","35513","151418","-279533","18960","117483","82262","-33661","-7682","158416","18028","-177037","70962","2396","-27722","-80704","110144","27095","-1547","201309","117026","-103810","-107285","51742","-89986","-95466","163578","25962","-5115","19893","159686","-108020","22188","-190448","59821","28869","-2247","-105343","-10127","-225249","61807","-12741","139939","-44100","-59726","-161275","-58840","30018","134610","38635","-156944","-129306","-11096","-106842","6664","849","214238","-141027","-73663","-267779","49282","188724","140943","-94584","18120","180388","147040","-14695","-143156","-84750","-24986","-59400","-72685","-18133","78227","-106844","-70572","-192622","-178650","144744","-117070","-63998","-18917","-202760","30070","-179450","69155","-25850","-30288","-56119","109026","163174","-65230","20324","-139630","-8028","-71416","102987","228126","-181242","60206","-197691","-3719","-219309","-18442","-185017","12562","230464","-74352","74705","197354","260498","-90740","-38922","46375","-77673","-58076","-95923","-103988","54851","-111186","-79889","115317","-321225","-101209","-248348","107457","-55635","7478","98069","78964","149542","-111490","-142342","-71503","7142","-46858","-4239","229982","-83858","131210","-233890","-50576","-128067","-51450","-112607","138534","-192036","-104127","151804","-30608","-389","-77895","-181369","179138","-54972","38644","172113","-149678","28420","12680","-111112","51270","-228404","-186560","44529","-99142","-203958","-91586","-226771","334932","-170821","-32585","-66663","120228","38990","-59408","46818","-87913","-107446","-164762","45824","-166886","-314043","-146540","-188112","182310","-2734","143526","-38939","-41466","-42724","12769","21519","-63368","-154094"],"derived":{"al":[[157,-1]],"fricke":-1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"157.4.a.b","letter":"b","dim":21,"charpoly":["62554906820512","219035053957980","-534638519740816","149500996778515","204565834404879","-79578057589126","-30437731639289","12933713966875","2093104121666","-1019488111238","-61419049406","43959513911","63480815","-1074332817","40602847","14458373","-999898","-92125","9878","103","-36","1"],"traces":["21","11","25","95","15","9","29","156","242","92","223","243","100","153","150","435","313","418","133","105","104","97","513","-16","556","231","742","284","367","74","518","1349","126","414","1286","1798","366","538","372","-474","340","-1632","1048","969","-891","-3091","688","-3178","522","-2187","594","-2467","1337","-2575","-1392","-1187","632","-3767","206","-4130","-2017","531","-2103","-2848","722","-8305","785","1757","24","-5583","224","2135","-1624","-1650","465","-2962","1964","-4106","1115","-1579","161","-1712","3652","-6699","-1126","436","3208","-616","721","-3242","-1318","-885","298","-1297","3004","-6738","-1868","-935","2939","-5193","2680","-595","-525","214","2662","-259","10126","-484","2468","3349","-668","530","3187","1582","2178","2195","3604","-2809","4178","-1721","6652","-494","7418","4726","930","-3472","6820","9872","2524","498","8510","-4041","1496","9610","676","4239","4096","-2822","986","6783","4892","2398","8336","4692","5360","1055","15023","5854","6605","-2754","3033","3531","7413","6317","18466","-91","-3297","5318","-223","-2738","-400","14849","2618","1016","-11365","4062","9998","-12468","-6027","5404","1963","9115","-426","-6939","-11670","15079","928","908","2540","-15968","-8871","3424","1694","-22588","-94","-9876","-3884","6900","-34667","-4670","4071","-31033","-10065","2603","-4204","3716","4550","-6758","-11088","-7422","-25174","-6486","16698","-559","-16580","16030","-11274","-10252","-9314","-19012","-8812","15270","-8866","-5562","-2180","-12701","-14652","5024","1918","-16367","-13006","-15448","923","1459","-21181","-815","2144","13929","-37180","22852","-614","-27678","8101","-18353","-7314","-5469","-10630","-9704","13888","-8522","-18282","5415","1949","-20508","-24731","25708","-7946","28841","-39158","16193","16134","-28944","-10970","1872","-26651","3259","-2433","11940","1884","14702","-18013","8645","27170","-57581","-42340","28290","-7956","25688","-20727","3597","-4629","21071","-25074","7058","25001","25062","-35158","39437","17752","-4744","9093","16115","10113","-2574","-46785","14117","18304","56387","-27324","10914","740","-5499","12991","24413","-6472","14339","-43826","23055","17986","28615","-31824","35416","16224","-5681","13556","62001","3490","67608","-33330","-4708","12334","17985","-20951","-1727","25051","41794","10828","13413","-6741","26257","10632","24590","47909","26729","-7198","38934","16564","15489","-12938","53255","21307","45130","-10712","28169","13804","11090","-8642","9395","8637","-16614","-1256","-9376","10240","31420","-29984","2051","59301","46238","-27678","36237","40620","49360","21555","6628","-8980","21940","-51987","45024","7989","-8712","-994","16024","37040","-37650","-18394","35407","2233","-33882","-23274","4439","7652","-20865","-11333","-49574","-5588","7883","-28158","-40392","6134","-48876","18272","-2511","11299","-99111","-20752","-1872","54478","21263","-26744","-941","-9586","-44402","-542","-27110","11503","57482","-26075","-18467","-45799","-35996","-14176","-19498","25600","-54456","-14609","-6339","39772","-16782","-54676","-90624","13132","-50886","-15504","-93071","17244","-28018","-29814","-27235","-24307","22792","-4495","-48746","45468","3707","-32611","70339","-5684","40379","-61088","-21888","24008","-73216","1318","-143105","48969","9972","-16832","29356","-16621","-77136","27033","11465","66558","-39553","12603","-69333","3590","44459","-12340","-108887","22996","-65825","29632","-83786","4038","83299","-25891","-4009","24946","-32344","25354","37451","41375","-123642","7358","-34518","16285","19772","8348","-49825","-3925","-46058","-5842","10836","28277","-75177","54919","88484","-4593","-38472","-29072","-72891","58253","75444","-16630","93115","14660","-63589","-1304","-6420","78546","75440","-8548","-145912","-24091","75355","-30230","-23919","-40754","-25869","-11640","-24528","21483","-73852","20614","-108911","51111","99852","-69441","9668","18714","-47343","20982","33966","47600","716","-31246","-58342","65740","13404","21956","-120152","63967","-84179","-16594","66917","40436","-104359","4162","-66841","27660","-11664","45224","-97357","-15438","37596","-17732","47035","21846","5637","-11611","-57727","80042","18555","-40916","31889","75023","-44307","-74146","-28969","4612","54048","44152","-92960","63624","90129","-12488","148049","-12584","-64331","27028","-291","89020","55658","-21844","-107087","-78273","68649","-17680","64060","25485","-63706","-10726","-80598","46769","59362","62987","30872","68080","19295","17274","56705","73966","-145834","37554","68352","13298","249734","-5000","-45176","101832","94304","31717","-167423","62566","37929","24282","144716","-5609","65056","36771","2159","77768","28911","-6179","67680","11426","-46755","50162","135946","28306","172297","54677","-126771","17224","89186","19707","98179","27851","55973","35248","65079","74352","-36634","61963","80732","68654","-14915","-49396","-22802","101912","-24274","105558","54783","27262","16848","-44850","-32391","-118258","90083","88565","54579","39600","-116347","42736","42812","4776","208843","-12844","-152754","-74332","32029","35172","-39265","-82876","-51367","-42292","80700","77755","-79406","-20734","28460","-56532","6616","-21522","51691","81918","50970","-45855","-21436","-143970","-58218","49776","-327150","12131","67094","55778","-13396","-71956","18533","-74924","-8704","86198","-82751","-76760","-136671","-141314","48746","-30286","156606","-45430","-153879","41388","59893","-22432","152299","-17114","-14694","-31870","-23635","82367","-23562","-81048","-45276","-130888","-64989","-58614","243245","-24378","-44802","-91481","116220","-18888","-224348","68","-49439","-11796","19351","-30949","-98912","17426","-104384","-163508","-38005","-14273","-179309","-201258","-72903","44828","8461","24974","40409","-46612","-176059","-159701","51822","31128","12315","92379","-91462","-91706","132783","21108","-219753","16120","-39218","5158","47947","-46400","236151","-265591","-22632","91782","-94026","-5497","-266190","15405","12401","51484","-8132","79512","-61542","-30564","-77119","-136248","178988","70898","-194547","-49591","-244468","-67702","-100813","35820","94367","-149460","-57924","127216","139420","-50508","28619","-164490","-178203","-109456","-74649","-2355","13528","42926","143462","15540","-61999","-33634","152514","-10862","-37292","-161724","-10048","11646","263850","-78334","-125391","-36277","214028","110604","-165293","103001","75749","-180630","-57437","26278","-80985","-105544","12503","65526","-50988","-49540","64691","-42586","7500","-44138","177000","-5588","183487","-114295","-69499","88858","-99546","203075","-156620","10478","48458","-285298","-21514","173431","256425","-53294","-61116","96516","35564","-205563","-63293","85278","-31335","53481","-157901","34087","22215","-70777","107706","-62310","-68165","59656","189514","-50224","-64113","-185868","99518","97190","103860","-39274","-175803","-7586","-43447","-72711","-131903","129014","59244","53455","-21424","132160","12654","-254736","79465","-45898","-59162","149530","374926","-341","17655","-114499","-106050","-137550","185594","7944","-117344","12554","122514","-93213","-62760","-113942","-23374","-218085","149412","202444","16121","-96178","184162","128362","-25856","11102","-52928","46288","-11537","-247902","81228","-14038","405173","160497","-20627","-1542","240037","6146","220292","45856","71437","-23066","-158008","11126","421232","-4285","255509","58412","62717","46136","161385","-98910","-89709","-106903","23263","-32677","-21456","-35719","358481","16738","194637","-66360","58010","29536","-155218","61377","20988","68500","-1413","-268186","-209830","275538","392778","140618","265905","58650","-39137","-339334","-114240","50169","209216","235980","301643","174919","174375","136262","282420","-27233","301735","212164","-58208","-43720","330880","72330","86618","43184","150771","12392","116358","65610","-53161","-221304","-3949","203159","183333","6580","-224946","75016","82914","-64173","310554","48382","-116692","-28186","-80275","-6706","353596","-117394","151252","-86618","126093","220710","-237570","-86035","151767","-339268","33958"],"derived":{"al":[[157,1]],"fricke":1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.12,"computed":"atlas","estimate":{"seconds":0.343,"low":0.209,"high":0.594,"bytes":2120816},"url":"https://sagebrush.space/atlas/mf/157.4.a"}