{"label":"83.2.a","level":83,"weight":2,"dims":{"new":7,"cusp":7,"eisenstein":1,"modsym":15},"old":[],"T":[[2,1],[3,1]],"status":"proven","checks":["dim M^+ at levels [1, 83]: [0, 8] (certified at ell = 2147483323)","T = [(2, 1), (3, 1)]; h of degree 7 = 1 x 7 (phi(ord eps) x dim S_k^new); 1 primes, 0 rejected"],"newforms":[{"label":"83.2.a.a","letter":"a","dim":1,"charpoly":["2","1"],"traces":["1","-1","-1","-1","-2","1","-3","3","-2","2","3","1","-6","3","2","-1","5","2","2","2","3","-3","-4","-3","-1","6","5","3","-7","-2","5","-5","-3","-5","6","2","-11","-2","6","-6","-2","-3","-8","-3","4","4","0","1","2","1","-5","6","6","-5","-6","-9","-2","7","5","-2","5","-5","6","7","12","3","-2","-5","4","-6","2","-6","0","11","1","-2","-9","-6","14","2","1","2","-1","-3","-10","8","7","9","0","-4","18","4","-5","0","-4","5","-8","-2","-6","1","-6","5","-4","-18","-6","-6","-18","-5","-17","6","11","3","15","2","8","7","12","-5","-15","6","-2","-5","2","-5","12","-6","13","3","8","-12","-4","3","-6","2","-10","15","-14","-4","-2","-6","0","-2","-18","2","14","0","-2","11","-16","-1","9","6","-10","9","-10","-6","10","-14","-6","10","12","-1","-22","2","6","1","21","9","23","10","-4","8","21","-7","3","-3","-5","0","-6","-4","-26","-18","-5","-12","22","5","15","0","-15","4","-3","-7","2","8","-12","-2","11","6","0","-3","2","6","21","5","4","4","8","6","6","6","-8","-6","-2","18","16","15","-15","17","0","6","-30","-11","-16","15","2","-15","-28","2","-10","-8","9","-21","18","-12","0","-5","-14","15","-8","-2","-1","2","-16","-5","-4","-2","-12","15","1","-12","8","-6","-12","-13","10","-17","-6","-8","33","-12","14","4","-6","-9","-12","6","0","2","10","10","-32","-5","-18","14","-3","-4","10","2","-10","18","0","0","26","-2","4","18","6","10","8","-14","8","0","-6","2","-10","-33","15","16","24","-1","24","-9","6","-2","-10","10","20","9","4","10","0","18","11","-10","-12","-14","3","6","-21","-14","18","-12","10","-1","6","22","17","-6","0","-6","-22","1","22","-21","4","-3","2","-23","-15","10","15","4","15","-24","-8","-21","14","-7","23","-3","-30","-15","-1","5","-4","0","15","6","33","12","-15","26","2","-18","0","5","-14","4","4","-22","-18","5","-11","-15","-12","0","42","15","16","4","-13","3","-29","-3","18","-2","16","8","4","12","-20","6","4","-11","-28","6","2","0","6","1","-18","-2","-30","6","-2","-21","-33","-15","-21","-4","14","4","-15","-8","2","30","2","-6","27","6","-38","8","0","18","-5","2","-15","18","18","-16","21","-5","-16","15","-14","17","-8","0","-8","-18","-4","30","13","-11","0","16","16","-21","-2","-2","-6","-15","-9","28","-36","-6","30","10","25","-8","20","-9","-5","7","10","-18","-12","-12","6","0","-10","15","-24","14","-2","15","-12","8","21","-10","66","1","-12","2","16","16","-16","15","22","4","-10","-2","-35","12","12","-5","-6","-1","-9","-12","-21","-8","0","18","12","12","-23","-13","-33","-10","0","11","10","6","8","-8","0","-33","-21","36","-14","-14","29","4","-3","6","25","3","-7","12","-10","6","12","0","36","-6","6","-10","6","10","-26","32","26","-25","34","18","13","14","-10","3","-14","12","-42","-10","-22","2","-26","10","48","-6","-15","0","21","0","-30","-26","-3","6","-18","-4","16","18","3","-6","4","-14","-18","-8","-2","-14","3","-8","18","0","-24","6","-12","2","10","10","-11","11","-15","-15","30","16","0","-24","12","3","42","-24","4","-9","4","-6","24","-10","-21","10","0","10","-8","-20","-4","-27","11","-4","23","10","-20","0","0","-6","-19","-11","-6","-10","-55","12","-12","42","8","-3","-26","6","-12","21","-4","-6","8","-18","8","-12","-16","-10","-42","3","15","-6","15","22","24","-17","8","2","0","0","-12","-6","0","22","30","-3","12","-22","28","-21","16","-4","15","-15","-23","-2","-5","-23","-8","15","24","-30","28","-15","28","4","28","-15","10","8","-36","8","-35","-21","18","-14","4","21","-10","-23","-18","-3","22","30","-22","21","0","1","18","5","6","4","-28","0","-20","-15","36","6","8","-33","44","-4","12","15","1","26","7","-2","23","54","13","0","-40","5","-1","14","4","20","-6","-4","-16","-22","12","18","-36","-15","32","11","2","-15","54","12","40","0","-8","-42","-18","15","23","-16","12","-12","12","13","51","3","20","29","-30","17","-16","-18","6","-2","30","-16","-5","-24","-33","-4","-4","12","6","20","-35","-2","-20","-4","52","-11","6","28","-45","-18","-30","-2","12","0","-24","-6","0","5","0","18","0","-2","-24","30","-10","-18","-28","2","-20","-21","32","33","44","5","-16","21","-36","-4","-32","-14","36","-12","3","15","-32","-8","-6","-2","-10","-42","10","-2","-42","-6","25","-27","-45","-18","20","38","0","8","-46","0","6","-6","-26","5","44","2","1","15","8","-54","-49","-18","41","-16","-6","-21","37","-25","-42","16","-8","15","42","14","12","-51","16","8","-36","0","-14","8","6","6","21","4","-46","30","10","-13","48","33","-39","0","3","16","0","-16","12","-9","-24","2","-35","-2","30","6","-24","45","52","9","-47","28","12","36","3","2","-3","-30","10","10","12","-25","20","24","-20","-20","-12","-9","11","5","8","35","-35","-10","4","-18","0","12","-30","36","12","-6","-11","0","-25","10","8","-5","30","24","32","14","0","2","-3","-45","-27","12","6","8","21","-21","42","14","-6","-66","36","1","-4","12","22","-6","-10","-16","-22","16","6","16","-6","-5","-19","-22","0","4","34","10","-44","6","-22","35","0","12","32","-12","1","-25","22","6","0","-1","-9","9","-55","36"],"lmfdb":"agrees","curve":{"cremona":"83a1","lmfdb":"83.a","ainvs":[1,1,1,1,0],"rank":1,"torsion":1}},{"label":"83.2.a.b","letter":"b","dim":6,"charpoly":["2","-4","-20","33","-11","-2","1"],"traces":["6","1","1","7","2","-7","3","3","3","-6","-3","-9","14","-15","-6","1","-5","-12","-4","-20","-2","-1","-5","-17","14","-2","10","9","-1","18","3","17","2","15","-10","-8","39","-6","-8","-18","-1","17","-8","27","10","-12","-12","7","11","35","-24","36","14","19","-24","-23","-10","25","-17","0","-5","5","-11","9","-8","-39","16","-15","8","-10","-26","10","-6","23","-45","-28","6","-18","-12","-60","-34","10","6","41","18","16","-3","-17","-22","-4","-2","2","34","-8","-4","-19","6","-30","-18","41","-8","35","4","78","-48","-46","-24","15","21","38","30","-39","21","78","18","-27","28","-27","7","62","-5","41","-6","-43","24","-6","15","35","-6","-96","25","51","50","-14","36","-17","-28","-36","-24","24","40","14","-22","10","-22","24","22","41","0","-33","-13","2","-31","-31","28","-68","34","-46","2","-62","-4","21","18","-8","-8","1","39","-51","30","10","-8","-48","15","55","-35","19","18","-84","-44","-8","-18","-66","45","-76","8","-9","-14","-30","-54","-76","23","-53","25","40","32","-24","13","6","-5","45","-42","10","18","-3","26","-12","-15","68","-60","58","52","66","-8","42","24","73","-58","25","48","-40","-42","-95","-6","51","-23","-13","72","-16","-15","140","96","15","-36","-28","-24","-75","6","27","2","124","-23","-92","-19","-3","24","-10","0","-15","1","24","16","52","68","95","-40","-11","-18","52","-20","-132","-19","28","58","-33","-44","54","-8","94","-38","-42","-18","-55","-72","-22","7","100","63","-46","38","98","18","-12","24","34","-16","50","-62","-22","-37","-90","76","26","3","32","74","-21","-34","60","-74","-67","10","59","-80","-44","-106","10","-22","9","-58","46","8","-90","-43","10","-4","-44","37","-18","-60","-4","-92","-34","42","-73","38","-6","-36","50","-76","18","14","7","12","-81","32","7","-14","59","27","80","-37","8","18","-68","-62","51","-34","-65","29","-81","74","33","5","33","-84","-24","19","-54","27","48","38","-14","51","16","-92","-29","-34","-60","27","46","96","-39","87","51","-8","76","-12","-47","-14","80","19","105","-7","75","-34","-34","-36","-80","30","172","0","-34","8","-23","52","38","71","-96","-58","3","11","-90","-14","70","-8","101","21","23","-7","-12","-2","0","-31","10","2","90","6","70","81","-44","52","-128","70","22","41","-34","-14","-26","10","56","-9","37","-22","63","36","35","-100","-92","-62","-54","32","-30","-1","-39","60","96","16","-11","62","-28","-26","11","-37","-28","88","-18","52","-30","0","68","22","-133","5","9","52","62","-42","-52","-8","-64","16","-103","-24","46","-72","-75","14","-28","-13","6","34","53","101","-12","-4","-14","-34","19","8","4","10","-66","48","-76","-58","9","18","-7","-23","28","23","-40","-72","-6","-4","-106","-101","9","-15","-70","-98","-91","-46","-70","64","20","-38","-67","30","-124","17","2","43","66","22","106","-26","-79","9","-76","17","-40","38","44","44","38","56","-42","-45","-72","-34","-44","54","-23","38","86","-29","-38","-19","81","130","60","14","-82","-16","148","80","-6","-100","36","6","80","7","-74","54","-78","-56","-18","-44","32","-30","68","-54","0","21","-54","48","-60","42","20","3","-16","36","120","72","54","-100","18","-40","178","96","25","7","113","18","12","16","-72","-2","-43","22","88","0","25","4","-2","-75","18","-26","-86","60","32","116","36","50","-39","57","72","-115","28","-37","-76","40","-20","-14","-59","18","20","-44","20","50","-54","94","-7","-98","62","18","73","-66","-6","-30","102","-56","60","-48","-82","50","-29","-6","86","-76","64","-14","-19","-98","42","50","76","92","24","0","-14","-60","3","116","-78","-116","53","-20","52","12","75","-57","-54","130","145","-44","-75","-80","-6","-60","9","-20","28","-72","99","50","-96","96","-112","19","45","75","-58","-156","-21","-14","-31","-84","-85","-23","70","-120","-61","172","-95","-8","89","-48","20","28","-60","0","81","-140","-116","-64","177","-44","52","-42","-27","-94","0","-47","0","-75","-54","57","-108","82","-53","29","134","-42","-60","88","2","-63","-144","-116","-134","14","117","-120","7","3","-123","12","-72","-44","142","50","34","-30","-37","61","-80","67","152","-52","-23","29","33","-40","-93","-110","-69","-38","126","22","-12","108","16","-23","-56","66","80","-48","104","112","114","-33","-66","24","-28","41","-117","42","84","10","-66","-32","-118","-48","26","-80","126","-92","43","34","50","24","38","-122","-30","52","130","114","46","-60","-105","118","-85","-28","11","64","69","-22","-32","-36","118","12","184","6","49","-20","54","34","-6","18","20","-19","-154","-54","-128","34","139","89","-106","3","-142","-6","-30","-70","24","50","18","-26","-19","48","90","-41","153","52","-6","61","-110","51","160","-87","31","-13","-1","12","24","80","43","-16","-14","84","-47","26","68","48","-106","150","32","-86","-24","-33","-22","84","-40","-60","179","-46","-57","-30","120","-12","54","-24","4","80","-51","112","-42","4","-24","-68","76","34","-147","-52","-31","-17","172","-22","60","-19","24","-3","62","160","-132","36","-57","-16","56","-50","-28","-84","67","105","-13","72","21","87","-142","62","8","34","-48","82","-16","68","-234","20","-88","-107","-38","-19","-135","34","24","-26","80","84","-238","-68","89","19","-28","26","-72","-87","-23","96","16","-45","34","-94","95","-26","-174","-16","-46","102","56","-106","-42","42","-184","-100","157","15","-74","28","68","-53","62","224","54","-14","-97","-150","-48","16","48","-37","-117","48","30","18","-9","-55","33","50","-216"],"lmfdb":"agrees"}],"seconds":0.156,"computed":"atlas","estimate":{"seconds":0.205,"low":0.125,"high":0.354,"bytes":1853788}}