{"label":"757.2.a","level":757,"weight":2,"dims":{"new":62,"cusp":62,"eisenstein":1,"modsym":125},"old":[],"T":[[2,1],[3,1]],"status":"proven","checks":["dim M^+ at levels [1, 757]: [0, 63] (certified at ell = 2147478481)","T = [(2, 1), (3, 1)]; h of degree 62 = 1 x 62 (phi(ord eps) x dim S_k^new); 6 primes, 0 rejected"],"newforms":[{"label":"757.2.a.a","letter":"a","dim":29,"charpoly":["259002","1651455","-4317219","-41821800","-36685867","184529903","314482475","-256683136","-803818465","-43093729","975273994","476830936","-589007699","-538092861","123543980","281419743","47014821","-70584748","-33273301","4844554","7049546","1256333","-472466","-238720","-24935","7887","3023","448","33","1"],"traces":["29","-12","-21","26","-11","-2","-10","-30","26","-8","-22","-33","-21","-8","-10","24","-41","-16","-24","-19","-6","-3","-27","17","20","-7","-69","-7","-17","21","-4","-67","-5","17","-75","34","-13","-33","-3","-13","-25","1","-39","-25","-8","7","-54","-47","25","-40","5","-47","-43","20","-24","-25","6","17","-69","-11","-3","-59","-28","52","-7","21","-27","-87","-11","56","-9","-12","0","11","-58","19","-55","32","1","-9","65","30","-135","31","14","24","-36","18","-28","4","10","-20","-9","46","-60","109","8","-48","-6","52","-25","85","-29","16","83","65","-92","-45","17","29","11","66","-16","110","7","31","-16","68","-26","107","57","26","-16","109","3","92","-1","-76","75","97","-107","100","6","26","9","119","19","94","-23","-47","98","49","-98","179","29","56","-47","30","7","154","46","5","-28","125","-67","110","-18","78","45","102","44","96","-15","-6","136","136","-114","97","70","92","-35","29","-35","96","47","24","112","54","-58","142","29","134","-29","92","1","164","-42","-5","117","149","-21","10","23","16","-24","86","25","26","17","35","72","61","-137","120","13","59","22","-100","28","1","-32","-72","3","90","-43","38","-5","-5","-63","39","21","-32","-39","-58","41","31","-210","57","49","-31","8","13","-23","-6","-34","-73","-33","-70","35","-56","28","-16","-223","-53","8","-99","-10","-118","121","-117","-148","-142","-43","8","-27","108","-120","18","-39","-32","61","119","-86","-93","59","-119","6","-179","33","174","-27","-186","48","-1","-37","-184","2","-64","63","62","-23","-43","-61","63","66","-37","-29","-263","96","-20","20","54","-82","82","4","-2","31","-25","-136","-130","21","-76","40","65","78","-50","-85","-120","125","-56","-19","35","-41","22","-155","-99","-22","-106","126","-75","80","-69","-33","62","-5","-54","14","11","12","-227","-29","-210","-13","85","-65","-94","13","0","-33","-4","-27","-167","52","53","62","-99","-169","-220","21","93","6","3","-66","-36","8","-202","124","-216","-16","-205","77","-53","-72","-38","-15","-84","-14","28","66","13","-63","-132","-27","80","109","-256","-17","-258","59","-190","-47","100","-61","126","47","55","-123","-3","78","-60","50","-218","57","-12","-161","-162","-39","-56","118","13","66","49","-53","-35","146","-139","-58","-187","76","140","-107","-25","-2","-126","-1","135","72","-7","-23","85","-55","-46","-1","158","-131","-135","-36","-172","239","-193","44","-239","33","118","-19","-167","-22","98","-4","78","64","-82","-195","45","118","-42","-41","94","51","-322","8","108","17","63","78","-149","15","-135","191","6","-27","103","35","60","158","-123","-188","-119","96","53","83","138","51","-96","-67","31","-70","-139","21","-26","-25","102","-98","-161","66","-30","193","7","123","103","-94","139","-7","96","-140","199","-3","-277","60","110","161","-72","-42","78","154","-44","-129","-84","87","-259","-31","-194","168","93","-72","-214","99","100","197","-65","-24","135","-106","-88","74","-116","35","15","92","-113","-102","47","-24","-39","79","35","131","-71","53","-540","-1","-60","88","240","-7","-478","-105","5","112","95","-23","255","126","36","99","-28","-3","-469","98","-40","52","62","-392","260","-22","5","-68","-72","82","-42","32","-77","90","-67","-5","-43","17","98","28","114","67","-87","89","91","151","-82","-205","-255","80","82","42","-77","102","18","198","-77","66","129","14","268","-157","101","11","178","98","-161","-71","39","275","-168","-96","-129","125","-27","305","25","97","-252","23","179","67","177","-118","303","139","43","-109","-402","75","81","-95","210","157","234","-99","87","9","-73","159","86","195","-156","95","211","17","-142","-24","148","10","7","-57","80","21","270","156","-200","207","20","-113","184","60","88","82","196","290","-92","-69","-163","337","-108","94","218","31","194","-89","237","49","-110","59","158","278","12","-183","-211","156","68","-29","-26","54","201","-62","93","76","68","238","-54","129","-173","40","-243","52","254","82","253","46","-34","-132","-167","133","19","116","266","98","102","108","-17","76","-67","86","194","60","-15","59","356","76","-52","-4","367","389","-178","-166","257","-71","252","232","-272","154","262","209","-77","171","152","132","124","97","185","-83","19","79","3","113","204","347","-252","-183","509","-29","29","156","257","-10","87","-113","16","162","-92","-68","-111","138","64","127","-289","-8","14","119","143","90","-98","108","112","17","6","-105","185","107","-85","128","64","58","110","25","134","43","-7","94","-475","-149","89","-18","123","-115","82","-221","337","-91","-96","19","26","-11","-549","-133","-41","102","22","28","29","-28","-172","85","-164","54","17","85","58","32","-465","-252","291","-76","446","-165","-259","-88","-38","-77","114","-26","-150","11","-293","24","86","-14","-106","3","-169","67","-301","48","153","-4","-354","54","132","-22","200","-210","-15","-22","130","-110","-341","47","360","-159","-131","-210","-165","38","-270","51","202","-17","19","-78","-656","113","184","314","-431","171","142","-75","83","-197","88","-275","-116","90","-18","-106","-2","12","191","105","-144","-175","-461","-174","127","-87","-21","13","9","13","44","21","-69","-265","-405","50","37","48","-110","-93","142","-22","-287","64","-150","130","193","-105","-236","-189","-284","-62","-4","-40","206","-211","132","-8","202","237","-423","-140","223","33","-25","12","157","-263","117","353","-138","-117","-167","-152","-15","37","34","-23","119","32","235","-176","59","66","-70","61","47","-209","132","-267","-84","-76","144","-123","-337","-179","-393","29","24","30","-168","-54","-209","37","6","-267","-64","-118","-28","53","58","-223","-143","86","272","22","-275","-115","61","-133","247","-257","294","55","-458"],"lmfdb":"agrees","derived":{"al":[[757,1]],"fricke":1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"757.2.a.b","letter":"b","dim":33,"charpoly":["-5685974","-62152787","151081785","1813747062","-724551105","-16018185238","2641635648","63381223004","-18809795286","-127541424298","60498341577","140097416494","-93720599504","-83904939912","79533059554","22902300393","-38913950742","1382114171","10864017551","-2786735709","-1555258587","788554961","56707769","-101672216","13197875","5741366","-1814249","-17490","80396","-11008","-595","294","-29","1"],"traces":["33","10","19","34","7","8","6","30","38","4","18","27","9","16","6","28","33","20","20","11","-6","-9","25","23","24","5","67","-3","17","-11","0","45","11","-5","73","18","-11","29","5","-13","23","-27","27","-5","-14","-35","78","5","13","-8","37","-13","11","-12","0","-1","-2","-31","75","-79","-17","-1","-12","0","1","-43","15","63","-15","-28","19","18","2","-17","38","7","17","-60","-7","-27","29","-14","117","-97","-46","-38","44","-72","10","-80","-14","2","-53","-16","12","11","0","6","-6","-60","53","-47","19","-32","-5","-43","142","27","-41","-15","-29","-50","16","-74","-21","13","22","18","-26","-133","-11","-2","28","-25","-9","-76","15","44","15","-99","117","-44","-58","-36","-71","-55","9","-34","-17","9","-34","-45","70","-49","-51","-10","33","-116","-11","-64","-18","71","14","-91","57","-122","-56","-38","-59","-66","-12","-42","-29","-30","-32","-38","70","-179","-48","-60","25","-59","107","-152","-81","-140","-32","-72","48","-188","-73","-14","-21","-178","9","-96","6","109","-75","-99","-25","-94","-41","-48","6","-2","13","-96","-39","55","-26","9","87","28","-59","33","-12","-6","-8","-143","34","-38","-33","-28","49","44","-25","-5","-47","-13","-31","144","-11","-80","-19","55","190","29","-41","-1","-40","9","35","-104","-22","179","-25","-14","35","-164","-6","38","125","-103","-80","109","-82","36","-11","167","76","-158","-87","24","-33","-24","74","2","19","18","51","29","78","-93","-41","3","26","153","47","-34","9","76","-20","-39","51","38","-28","114","-47","94","-9","-51","137","-29","8","101","111","155","-30","44","52","52","116","-42","26","6","-65","-61","138","98","-55","40","64","117","12","234","117","160","5","20","77","-79","11","-2","139","93","-20","-90","2","49","36","127","107","-62","-91","60","2","-13","-48","213","19","82","-117","49","63","-22","-23","90","-31","-66","83","79","-12","-153","-18","161","155","212","-63","51","22","-175","-18","110","52","68","-20","274","24","-169","-71","-11","172","-14","17","-28","22","14","20","33","73","-56","-49","-22","-61","278","13","46","-15","-54","-63","16","93","-48","-17","31","151","-43","-56","212","22","0","109","-64","209","-74","-21","152","-110","-119","-56","25","119","221","-106","97","98","161","-84","42","97","95","58","-52","-129","65","-22","33","81","121","-5","24","147","-2","23","89","-76","212","-81","201","56","177","15","-54","-163","115","0","106","40","26","-20","-38","153","-73","-102","84","-55","-66","-79","-172","4","54","69","-87","36","307","-83","207","111","66","-9","101","31","-42","-158","143","270","-121","-104","107","-31","92","15","124","121","-101","-184","9","21","-282","-125","18","136","171","-38","122","41","23","-77","167","124","23","-95","-152","18","13","35","3","-48","-22","5","120","210","-292","-118","-8","35","108","-15","21","41","116","-32","-143","-86","152","-145","40","71","75","-58","-201","144","20","-222","38","67","-197","-126","103","42","-81","-12","-139","-33","-15","-5","245","5","-56","-35","-26","-108","42","17","228","11","-33","-234","-167","-9","-129","-106","10","-5","34","-103","173","-158","-18","-204","0","396","-230","30","11","-196","94","-64","-262","-132","247","-66","145","-163","329","-143","2","-2","-118","-193","-187","-3","-161","-151","198","171","133","-180","-58","-84","-117","146","-276","14","83","-254","21","-106","242","-43","109","53","-122","-154","283","-23","183","-165","184","168","61","-161","-25","-79","29","-103","296","-89","-21","-157","-87","102","-245","-73","-129","-29","164","-119","-199","-171","-170","-1","-82","135","11","-201","-21","-177","46","-17","80","77","-89","-3","178","92","-60","-270","-313","-163","-164","-57","-82","-102","-46","-51","132","107","172","-182","-14","-50","60","-106","152","15","-15","-171","-72","42","-228","-3","-266","-77","15","53","114","-129","-154","70","24","141","73","-240","150","-229","-422","-174","263","-78","193","-156","78","34","122","-259","71","-48","73","-106","-190","-54","-395","-170","66","-28","121","-169","-83","-156","-52","30","-336","-160","285","-172","-65","62","-132","-220","43","11","-254","-180","486","-120","187","-55","-138","30","-103","-29","-206","-284","186","-30","-10","-109","-89","-217","24","20","-192","-231","-87","205","-5","-311","367","-195","156","-69","-72","173","-47","33","-35","-178","-147","-82","-193","27","-136","-222","-84","-72","33","-112","-220","139","123","-116","4","-87","-65","-244","-154","20","60","-17","-76","179","-211","-113","83","8","-10","-74","-74","33","-398","-67","-131","-148","325","49","-23","-160","21","-113","-188","259","55","-99","50","-15","246","-93","191","-67","-145","26","-134","-4","193","-150","24","-175","-52","-134","7","-3","-28","-84","221","148","-139","4","46","47","-49","166","-106","75","-150","-272","38","-45","267","-100","-218","-70","-130","-271","117","-145","61","16","-205","0","230","88","-90","22","-62","10","407","76","-114","-164","179","143","166","73","205","22","-201","-98","-66","-61","-182","99","-41","374","380","-117","76","-110","399","133","22","183","-329","-97","254","125","288","38","-234","-38","-108","-28","-221","-31","-268","153","285","114","143","43","-205","-51","97","-227","-48","155","375","87","-169","44","121","-56","-300","205","64","114","273","70","-142","-36","-19","283","248","-183","104","-70","128","-28","240","-79","18","-64","56","-11","-79","0","-205","127","-129","-118","145","93","113","283","246","159","181","-68","187","-151","114","37","-85","-4","-29","102","127","-62","-236","119","-29","205","40","85","404","-92","26","-191","265","205","-1","-35","-240","18","-34","102","143","341","34","89","-120","-18","-8","-43","30","111","117","-218","84","-90","91","65","-219","55","71","-77","48","-71","-10"],"lmfdb":"agrees","derived":{"al":[[757,-1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.244,"computed":"atlas","estimate":{"seconds":0.483,"low":0.295,"high":0.836,"bytes":2332300},"url":"https://sagebrush.space/atlas/mf/757.2.a"}