{"label":"751.2.a","level":751,"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, 751]: [0, 63] (certified at ell = 2147482501)","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":"751.2.a.a","letter":"a","dim":24,"charpoly":["-131","-107","6323","-10041","-54060","104890","199978","-394300","-420999","719985","577084","-695482","-521684","353949","290200","-85703","-92905","4933","15952","1580","-1294","-279","29","13","1"],"traces":["24","-5","-8","17","-16","-13","-7","-12","0","-10","-22","-16","-8","-19","-7","3","-51","2","-9","-31","-19","4","-12","-16","8","-29","-14","-14","-49","15","-17","-9","-8","-1","-20","-6","6","-7","-16","-23","-99","26","-1","-33","-23","-8","-12","-6","-7","12","13","15","-15","14","1","-39","-13","12","-18","28","-29","-10","2","8","-55","-2","17","-46","-29","34","-29","35","-36","9","16","4","-27","67","-33","4","-28","37","-21","33","23","10","33","32","-78","31","19","8","23","27","-26","-13","2","29","-8","25","-96","73","15","-57","-25","70","7","8","21","21","21","27","-29","31","42","-88","2","35","-24","131","-2","60","87","-10","-30","49","27","40","-73","99","-43","121","42","38","47","55","-58","63","-22","66","14","56","5","33","-11","-8","27","97","-60","38","19","36","-30","42","46","40","18","49","3","57","-91","86","34","-78","19","92","9","107","22","44","31","83","-53","129","32","3","15","61","-2","36","19","51","66","52","-75","91","107","57","9","127","-22","-14","15","-31","66","98","-11","23","-45","50","-40","73","77","97","68","-61","43","24","-172","92","21","16","3","-28","20","72","-35","-35","49","20","-13","-28","45","-94","-61","-58","15","-44","-22","37","15","87","-77","-50","39","1","25","40","-19","-49","-66","12","40","-128","-23","33","7","-102","-54","17","-29","-26","46","66","-2","-15","-107","-39","-25","-35","-40","42","-8","-28","31","-25","71","-107","-114","-122","30","-60","-61","54","-40","-59","-22","-76","-38","-88","-78","-17","-21","-34","16","68","34","61","-13","-66","54","8","-39","-174","23","2","-33","-107","-80","-37","-27","26","1","-133","-80","-31","30","-98","44","9","-31","59","23","-27","107","-91","12","-130","27","43","-152","-32","42","-195","-39","-79","77","18","-213","11","0","-68","8","-217","25","92","29","-131","-64","101","-86","57","4","-9","32","-82","-7","14","-3","23","-22","-60","-113","-71","46","-129","108","-61","-21","-67","-47","129","15","19","-58","-47","6","-10","-170","-137","-18","79","27","-94","113","34","-54","-112","-19","-77","1","-19","76","2","-7","54","118","-194","-51","-118","-16","142","-42","-54","-42","-136","52","10","53","-72","-91","-95","92","-70","90","56","71","-125","-73","-12","127","26","-105","-32","-64","-157","85","-76","22","-182","61","26","4","-95","-153","19","62","-38","44","-31","1","98","2","12","-14","105","-12","23","1","77","-34","85","68","-195","44","-38","119","-67","-129","-105","22","78","-86","-65","130","-17","20","-192","45","-51","-107","36","167","-145","-55","-68","65","-67","-26","17","-60","124","-88","12","148","-130","146","-224","-73","119","-137","-44","112","-93","108","-29","95","68","-28","-136","-64","167","67","-92","173","-2","9","57","94","-107","94","105","-19","-254","66","29","109","12","31","-92","8","51","-94","-164","155","-77","12","-79","44","108","-243","-116","64","-3","34","22","82","-90","42","-115","55","-10","46","-132","157","0","6","10","44","96","12","-38","51","3","-261","-46","127","-78","40","-146","8","19","-23","-57","16","-101","86","-167","-19","218","-8","161","25","-101","29","121","117","-109","-203","-148","40","53","14","140","76","-72","-104","23","74","114","-58","230","-5","-141","68","99","14","-146","-22","40","34","223","-62","70","141","25","145","-209","16","-125","-123","139","94","-211","49","82","3","108","26","78","34","65","-32","41","163","255","65","-35","133","70","-80","94","115","82","-24","34","199","153","-55","31","95","212","-125","-13","22","67","-1","145","58","-105","-77","-13","4","-188","198","41","87","-105","-53","34","58","252","-30","-44","100","-132","15","-287","109","-102","33","-12","200","199","15","161","119","-23","17","52","29","269","-37","96","38","-2","88","16","97","302","-62","51","55","198","57","-55","155","-203","-178","-140","56","91","63","-115","189","108","264","208","118","138","-21","52","-14","69","26","219","52","-147","82","-107","117","-68","-126","-80","175","92","218","255","-1","-118","16","169","15","-202","119","169","142","235","-36","-11","68","161","102","-131","87","239","26","-223","66","-15","39","53","103","-51","-38","70","80","45","134","-11","-24","121","45","33","101","136","106","-66","113","-3","-267","-54","85","-10","102","-217","21","-7","-55","106","153","109","-26","41","-43","-65","19","-66","-59","-157","173","176","197","79","-24","-50","4","-181","111","-19","-1","35","-87","-109","132","-138","108","-323","79","-24","-33","51","153","240","127","190","-54","75","-296","132","-107","272","151","-239","-147","111","96","77","-62","95","22","-176","34","-192","41","-32","94","-10","-70","-89","12","108","-99","199","31","9","247","-168","62","-64","13","56","-132","-318","-11","-57","-29","123","-233","-163","48","-177","9","34","-101","31","-103","-348","-42","99","124","157","-49","-133","112","218","-138","-46","63","-92","119","85","-21","-127","-212","143","14","-132","2","-91","-277","150","46","-118","110","-95","-44","-188","-108","57","74","-42","112","-5","-62","-119","-5","-77","-39","-15","-237","85","89","-9","-64","-186","-107","-44","-132","-439","-81","235","-141","41","-47","88","127","-139","-117","-29","-108","-84","-8","-135","231","-76","-63","-245","-284","-118","-78","122","-146","-220","116","87","-31","462","35","-131","-5","54","-177","58","-45","-69","-93","-294","135","-121","64","154","17","-173","83","107","-1","-7","18","-115","-39","-74","167","-98","55","228","-128","-257","-26","179","-117","134","17","20","-172","-343","57","-42","28","43","99","-183","-36","-1","-71","142","178","50","-136","-140","-127","136","2","-106","71","-169","109","-144","-87","-111"],"lmfdb":"agrees"},{"label":"751.2.a.b","letter":"b","dim":38,"charpoly":["-1085345","709293592","-55586688469","327439200118","841002005390","-4202947152172","-7334084652264","14006583568918","22454201267031","-24080054431262","-35931594613852","26235747470086","35498615836986","-19931920935341","-23502194226605","11096980628149","10896440487095","-4640104521813","-3620133277754","1470435467368","869442539078","-352814344035","-150451094568","63598164970","18441152374","-8498856480","-1539807810","826048404","79871999","-56850797","-1831556","2663957","-43750","-79842","4218","1364","-109","-10","1"],"traces":["38","4","6","40","18","13","1","9","62","0","20","10","10","17","-7","32","61","-1","7","27","13","-10","4","38","52","25","18","-22","53","-13","-5","12","8","-7","24","53","0","1","0","-29","117","-22","-5","45","19","-24","32","-4","71","3","1","-3","27","46","-7","21","11","-40","26","-68","37","34","-22","1","61","-34","-25","88","-5","-66","3","-52","24","63","18","-28","21","-49","-29","38","106","-37","9","-31","3","-26","5","-82","120","-63","-33","-40","-41","-17","22","1","12","-34","-2","-42","134","-83","-37","21","7","-20","23","-56","-1","-39","-35","-109","43","-109","-38","32","-20","-57","8","-97","60","-14","-13","-102","54","-83","-41","-35","63","-81","113","-87","-30","24","-97","-71","2","-125","-6","6","-58","-72","-11","-70","1","14","-75","-89","6","-144","-49","-60","126","-158","-34","-136","-40","-67","-45","-125","141","-169","-74","144","-141","-58","21","-229","34","-124","-49","-105","33","-107","-104","9","-45","-97","-10","-210","-11","-89","-94","-140","105","-125","-25","12","-35","-86","6","-122","-3","70","-36","33","47","-77","-29","-28","64","-59","21","-27","-12","57","-77","21","244","-84","-39","-14","33","-44","80","114","-43","-6","21","20","19","-154","-43","14","19","102","-1","28","4","72","-47","-69","153","100","-33","37","1","24","45","-13","54","-87","30","133","11","57","-121","124","94","61","89","-192","52","62","-38","-94","23","-37","-9","62","116","-2","40","52","35","-15","-103","67","216","74","46","108","-101","12","-44","-13","-88","-23","-46","98","92","91","25","62","-26","4","-74","-74","145","24","-54","54","33","318","-121","184","-49","186","72","47","-35","-50","57","-21","156","-41","-14","118","28","1","137","-97","79","73","-19","17","10","220","-81","86","168","-36","-40","300","71","-91","-85","-88","243","-1","-86","-16","-14","107","41","84","-15","140","-64","-11","46","-95","-28","-6","28","106","5","194","-21","139","-96","8","73","-27","-82","125","-46","-21","51","127","73","55","-41","-177","-8","-31","-42","-82","388","126","4","23","-15","198","-135","-98","144","212","-53","95","95","-23","0","188","-7","48","-42","200","43","188","-72","-77","24","-48","-36","168","-50","175","-87","-69","75","137","32","322","-36","52","-75","279","111","-120","-37","-50","-25","-176","82","129","1","72","54","118","-121","18","60","207","347","-43","-150","73","-12","169","-47","-220","36","-12","-150","-5","108","355","-27","-153","244","-9","-16","319","-48","96","-69","41","91","294","2","-20","-80","49","-32","-249","-62","54","-51","108","167","-102","-33","27","49","-10","-31","99","78","5","-168","40","52","188","-84","-118","-44","408","75","-273","27","-94","-88","-42","-12","171","-69","74","76","-70","-8","179","63","71","-105","-92","79","-75","-6","37","-42","-109","49","86","-74","-83","-103","-32","89","-208","-176","-60","56","262","-49","-85","-100","-233","-40","16","233","-160","0","225","-102","-54","-150","202","58","20","-193","260","24","236","-75","-70","-50","92","62","-494","-28","-70","53","-67","159","-242","-155","-44","214","164","-10","-329","-207","51","-24","283","-92","363","-187","32","-214","-41","-33","-81","-203","-9","-219","50","255","88","-146","-259","-138","68","-232","41","6","186","-98","190","70","58","-213","61","-96","127","-186","310","-78","-116","20","-331","156","278","-175","-205","-145","191","-60","-75","59","5","-264","201","131","78","-265","-31","-154","-14","2","181","-62","29","-201","-65","-5","105","59","-34","-222","34","73","66","-46","46","-209","-83","41","-257","-37","26","31","-85","-130","-85","-295","-131","-186","97","169","-233","-144","254","-66","49","-53","-36","67","-143","-346","-336","-42","340","-212","72","13","501","-33","78","-193","-114","-232","-139","-153","39","-165","329","-7","-288","-69","-491","-83","146","64","-53","86","212","-143","-306","-174","27","-213","-282","-51","-141","-395","337","234","226","-164","-155","-241","284","-99","-192","48","-4","34","-162","-77","10","-54","-109","-268","-19","-284","-17","-120","-119","-247","82","-74","168","-377","-128","-106","55","175","-128","-72","-350","-241","120","133","-211","-230","-55","-22","195","56","-363","-116","-235","-545","-241","114","327","-50","-90","-255","-243","-91","-27","22","-158","-352","161","-58","-139","38","-165","-3","-187","-83","-160","-156","58","57","-93","275","-404","-119","122","-44","1","-115","11","-21","-306","-167","-1","-66","-379","7","71","-73","-30","-143","187","-99","-370","-39","-20","26","404","-52","72","167","53","-129","-13","129","241","-256","-94","-6","749","-85","-159","333","-91","37","152","7","-228","-184","103","348","-234","-151","-56","-89","117","-91","43","-72","1","132","45","92","-60","-30","-4","-131","-64","-2","294","128","-177","160","-152","261","-17","23","339","-153","369","-74","-20","127","-82","-124","30","-61","-305","65","-143","11","23","-44","137","-21","54","23","-57","275","244","16","-25","-14","-111","-161","407","24","96","-72","58","-21","100","3","-219","105","249","-238","-5","28","40","22","-315","441","-41","90","130","116","-121","-114","34","-12","-56","88","-72","-48","157","-22","-25","25","-35","113","-310","-51","-267","41","13","-148","248","-145","-142","246","425","-9","345","11","-173","239","-74","-127","197","43","85","96","-82","-84","-287","-227","-58","-17","711","470","350","-54","44","18","-154","-36","41","75","74","-33","109","269","-198","-101","189","131","-27","99","462","15","-205","-12","42","-9","609","171","-185","-93","-179","314","87","15","-174","215","140","27","396","292","-36","298","119","77","-186","-165","-32","-76","181","-71","-90","-28","-155","45","101","-82","475","237","-234","90","-22","104","318","-251","182","-134","386","131","599","63","-100","65","166"],"lmfdb":"agrees"}],"seconds":0.243,"computed":"atlas","estimate":{"seconds":0.482,"low":0.294,"high":0.835,"bytes":2332030}}