{"label":"117.2.a","level":117,"weight":2,"dims":{"new":5,"cusp":11,"eisenstein":7,"modsym":29},"old":[[39,3,2]],"T":[[2,1],[5,1]],"status":"proven","checks":["dim M^+ at levels [1, 3, 9, 13, 39, 117]: [0, 1, 2, 1, 6, 16] (certified at ell = 2147483629)","T = [(2, 1), (5, 1)]; h of degree 5 = 1 x 5 (phi(ord eps) x dim S_k^new); 1 primes, 0 rejected"],"newforms":[{"label":"117.2.a.a","letter":"a","dim":1,"charpoly":["3","1"],"traces":["1","-1","0","-1","-2","0","-4","3","0","2","-4","0","1","4","0","-1","-2","0","0","2","0","4","0","0","-1","-1","0","4","10","0","4","-5","0","2","8","0","-2","0","0","-6","-6","0","-12","4","0","0","0","0","9","1","0","-1","-6","0","8","-12","0","-10","-12","0","-2","-4","0","7","-2","0","-8","2","0","-8","0","0","2","2","0","0","16","0","8","2","0","6","-4","0","4","12","0","-12","2","0","-4","0","0","0","0","0","10","-9","0","1","18","0","0","3","0","6","-12","0","-2","-8","0","4","6","0","0","-10","0","12","8","0","5","2","0","-4","12","0","-16","3","0","2","-4","0","0","8","0","-6","-6","0","12","-8","0","0","-4","0","-20","-2","0","2","6","0","4","0","0","-16","-8","0","-18","-8","0","10","0","0","8","6","0","4","8","0","1","-4","0","12","-6","0","4","4","0","-2","-4","0","-10","4","0","0","4","0","8","0","0","0","-8","0","18","-10","0","-9","-18","0","8","-3","0","-18","-40","0","12","0","0","-1","0","0","-20","6","0","12","24","0","-16","2","0","-8","-2","0","4","20","0","-6","20","0","-10","0","0","30","14","0","0","12","0","-8","24","0","10","-5","0","2","-18","0","0","12","0","-12","12","0","0","16","0","-17","-26","0","8","2","0","4","-24","0","12","0","0","8","-22","0","-12","2","0","6","4","0","-10","-12","0","24","10","0","12","0","0","4","24","0","-13","20","0","-2","6","0","24","-6","0","-6","0","0","48","-4","0","0","4","0","-16","-16","0","8","0","0","-6","18","0","-8","-26","0","-40","-14","0","0","0","0","-1","-8","0","-18","0","0","-16","4","0","-8","16","0","18","-1","0","-4","-16","0","-8","-36","0","6","12","0","-26","-4","0","20","2","0","0","-2","0","4","-24","0","-19","10","0","4","-4","0","16","0","0","-4","24","0","-26","-8","0","0","10","0","-24","0","0","8","16","0","-32","-18","0","-10","-22","0","0","27","0","18","-16","0","38","-8","0","1","-22","0","4","-18","0","40","8","0","34","-12","0","0","48","0","8","-5","0","0","-4","0","-10","20","0","-18","2","0","8","12","0","-24","0","0","34","16","0","2","0","0","32","24","0","2","4","0","-4","-4","0","-28","-22","0","24","-6","0","-20","8","0","2","10","0","0","38","0","4","-10","0","-14","-12","0","32","0","0","-36","48","0","0","-8","0","-24","24","0","-2","-10","0","-5","-20","0","12","-6","0","18","12","0","-20","0","0","-4","0","0","-24","-12","0","-12","8","0","-36","0","0","16","-10","0","-8","11","0","26","0","0","0","-8","0","-6","-18","0","44","4","0","24","-8","0","-23","-12","0","0","-6","0","24","-24","0","22","-36","0","30","12","0","10","4","0","4","6","0","-4","0","0","-32","10","0","-12","-18","0","-12","-8","0","-10","12","0","-12","-12","0","0","-34","0","-4","4","0","-24","0","0","-46","13","0","20","16","0","24","6","0","-6","-28","0","0","-24","0","2","26","0","-16","-6","0","0","40","0","-38","-48","0","-4","-10","0","-16","0","0","-4","0","0","-2","16","0","48","-22","0","24","8","0","0","-8","0","-19","6","0","18","4","0","20","24","0","26","32","0","9","40","0","-6","-2","0","-40","0","0","0","8","0","48","1","0","-8","-6","0","8","6","0","0","-28","0","30","16","0","-12","0","0","0","-8","0","-16","8","0","-14","-18","0","-1","-22","0","-40","12","0","16","12","0","12","8","0","12","-6","0","-24","6","0","-12","-24","0","12","26","0","-4","34","0","0","-28","0","-2","-72","0","-26","0","0","6","0","0","8","4","0","24","24","0","0","19","0","10","-10","0","8","-12","0","4","24","0","30","-16","0","0","32","0","32","-4","0","-24","-48","0","-12","26","0","-8","48","0","8","0","0","-10","-8","0","22","24","0","0","10","0","8","8","0","-16","-12","0","-30","32","0","-18","-10","0","-4","30","0","22","0","0","0","0","0","-9","36","0","-32","18","0","16","-24","0","-2","-38","0","-8","-46","0","0","5","0","22","-8","0","0","-4","0","54","30","0","8","40","0","-8","-16","0","0","-34","0","-12","22","0","0","0","0","-48","-4","0","-34","-8","0","7","-18","0","-16","0","0","4","-48","0","71","10","0","20","-2","0","-20","6","0","-2","0","0","30","-8","0","-36","46","0","-44","-24","0","0","-16","0","12","-34","0","16","-32","0","-8","-6","0","0","-48","0","-10","-32","0","-8","-58","0","-44","2","0","-4","48","0","64","4","0","-4","0","0","8","-12","0","22","40","0","12","-24","0","18","20","0","12","-20","0","-8","40","0","16","-2","0","10","16","0","-48","0","0","-38","0","0","2","-4","0","-50","-30","0","0","-14","0","12","-16","0","26","-32","0","0","14","0","0","12","0","-48","60","0","2","0","0","24","30","0","16","-24","0","-24","24","0","-15","2","0","-10","-36","0","-52","15","0","20","60","0","-48","-12","0","2","42","0","-8","18","0","-12","-16","0","36","20","0","0","0","0","16","-20","0","0","-16","0","-26","24","0","36"],"lmfdb":"agrees","curve":{"cremona":"117a1","lmfdb":"117.a","ainvs":[1,-1,1,4,6],"rank":1,"torsion":4}},{"label":"117.2.a.b","letter":"b","dim":2,"charpoly":["-3","0","1"],"traces":["2","0","0","2","0","0","4","0","0","0","0","0","2","0","0","-10","0","0","4","0","0","-12","0","0","-10","0","0","4","0","0","4","0","0","-24","0","0","4","0","0","0","0","0","16","0","0","24","0","0","-6","0","0","2","0","0","0","0","0","24","0","0","-20","0","0","2","0","0","28","0","0","0","0","0","-20","0","0","4","0","0","-8","0","0","24","0","0","0","0","0","12","0","0","4","0","0","-36","0","0","-20","0","0","-10","0","0","-8","0","0","0","0","0","-20","0","0","-20","0","0","0","0","0","12","0","0","2","0","0","4","0","0","-32","0","0","0","0","0","8","0","0","24","0","0","-8","0","0","12","0","0","0","0","0","4","0","0","28","0","0","-24","0","0","4","0","0","0","0","0","28","0","0","36","0","0","2","0","0","16","0","0","-20","0","0","24","0","0","-20","0","0","-24","0","0","48","0","0","0","0","0","52","0","0","-6","0","0","-32","0","0","-48","0","0","0","0","0","-10","0","0","16","0","0","24","0","0","8","0","0","0","0","0","4","0","0","-24","0","0","28","0","0","-24","0","0","0","0","0","-48","0","0","-20","0","0","-20","0","0","4","0","0","0","0","0","-48","0","0","38","0","0","8","0","0","-72","0","0","0","0","0","28","0","0","-44","0","0","-24","0","0","4","0","0","0","0","0","-8","0","0","-12","0","0","62","0","0","-20","0","0","0","0","0","48","0","0","32","0","0","-20","0","0","52","0","0","0","0","0","28","0","0","-8","0","0","-48","0","0","48","0","0","-10","0","0","-24","0","0","-20","0","0","60","0","0","4","0","0","0","0","0","-40","0","0","48","0","0","52","0","0","36","0","0","0","0","0","-48","0","0","-30","0","0","4","0","0","16","0","0","0","0","0","52","0","0","36","0","0","4","0","0","48","0","0","0","0","0","-20","0","0","-96","0","0","-48","0","0","4","0","0","50","0","0","4","0","0","48","0","0","-20","0","0","-8","0","0","0","0","0","-24","0","0","-20","0","0","0","0","0","-40","0","0","0","0","0","4","0","0","-20","0","0","-56","0","0","-24","0","0","0","0","0","4","0","0","-48","0","0","12","0","0","-20","0","0","0","0","0","4","0","0","0","0","0","56","0","0","-12","0","0","-20","0","0","-36","0","0","4","0","0","2","0","0","4","0","0","0","0","0","-96","0","0","-20","0","0","28","0","0","-24","0","0","0","0","0","-32","0","0","-40","0","0","96","0","0","72","0","0","0","0","0","40","0","0","24","0","0","50","0","0","8","0","0","0","0","0","-24","0","0","-20","0","0","72","0","0","-8","0","0","60","0","0","-16","0","0","-8","0","0","16","0","0","-72","0","0","0","0","0","-12","0","0","40","0","0","48","0","0","52","0","0","0","0","0","0","0","0","48","0","0","8","0","0","-20","0","0","0","0","0","24","0","0","-68","0","0","28","0","0","-80","0","0","0","0","0","4","0","0","24","0","0","52","0","0","-72","0","0","50","0","0","4","0","0","76","0","0","0","0","0","-6","0","0","0","0","0","28","0","0","-48","0","0","-24","0","0","28","0","0","0","0","0","-72","0","0","52","0","0","-36","0","0","96","0","0","0","0","0","-20","0","0","2","0","0","-40","0","0","-24","0","0","0","0","0","-80","0","0","-20","0","0","-96","0","0","-96","0","0","-20","0","0","8","0","0","24","0","0","76","0","0","-24","0","0","0","0","0","-36","0","0","-16","0","0","-20","0","0","64","0","0","0","0","0","-68","0","0","-72","0","0","-44","0","0","0","0","0","0","0","0","48","0","0","-8","0","0","24","0","0","4","0","0","0","0","0","-40","0","0","-60","0","0","100","0","0","52","0","0","-20","0","0","72","0","0","-24","0","0","30","0","0","-44","0","0","0","0","0","-20","0","0","-32","0","0","144","0","0","-120","0","0","0","0","0","48","0","0","52","0","0","-24","0","0","32","0","0","0","0","0","-8","0","0","24","0","0","4","0","0","2","0","0","0","0","0","24","0","0","38","0","0","16","0","0","4","0","0","120","0","0","-92","0","0","-24","0","0","-80","0","0","132","0","0","0","0","0","8","0","0","28","0","0","48","0","0","-44","0","0","0","0","0","88","0","0","72","0","0","-64","0","0","4","0","0","0","0","0","-24","0","0","0","0","0","24","0","0","88","0","0","0","0","0","-72","0","0","28","0","0","-8","0","0","-96","0","0","-20","0","0","-72","0","0","-12","0","0","72","0","0","52","0","0","0","0","0","96","0","0","-96","0","0","-20","0","0","48","0","0","0","0","0","-12","0","0","-54","0","0","-20","0","0","4","0","0","0","0","0","-16","0","0","100","0","0","-48","0","0","24","0","0","0","0","0","4","0","0","-32","0","0","24","0","0","-20","0","0","0"],"lmfdb":"agrees"},{"label":"117.2.a.c","letter":"c","dim":2,"charpoly":["-1","-2","1"],"traces":["2","2","0","2","0","0","0","6","0","-8","4","0","-2","-8","0","6","-4","0","0","-16","0","4","8","0","6","-2","0","-16","-4","0","-8","-6","0","12","16","0","-4","8","0","-8","-16","0","8","4","0","8","12","0","2","6","0","-2","4","0","0","-8","0","-4","-4","0","4","-16","0","-14","0","0","8","28","0","16","-4","0","12","12","0","16","0","0","0","0","0","-24","4","0","-32","24","0","12","-24","0","0","8","0","-4","-16","0","-4","2","0","6","-4","0","16","-6","0","4","0","0","-12","-16","0","0","-12","0","0","-4","0","12","-32","0","-14","-28","0","-24","0","0","0","-10","0","8","16","0","-16","0","0","4","16","0","8","16","0","-4","-4","0","0","28","0","28","24","0","-24","8","0","-16","16","0","-20","32","0","-8","0","0","32","-32","0","20","-4","0","2","-16","0","40","12","0","0","12","0","-16","24","0","28","8","0","24","-32","0","-8","-20","0","-16","16","0","-12","-20","0","2","16","0","32","18","0","12","0","0","16","32","0","-6","0","0","-24","4","0","-32","-32","0","16","-44","0","-32","4","0","-8","-8","0","-44","12","0","20","-32","0","-12","20","0","32","28","0","-16","-4","0","12","-14","0","-60","0","0","0","-32","0","16","0","0","16","-16","0","-26","20","0","-32","16","0","16","-24","0","0","-16","0","-8","-36","0","-16","-12","0","8","12","0","-4","40","0","48","-48","0","24","-4","0","-4","16","0","38","16","0","44","24","0","-32","4","0","32","-8","0","-32","-48","0","0","64","0","-40","-32","0","48","-24","0","12","-20","0","64","0","0","-8","16","0","-32","32","0","-6","24","0","-56","32","0","24","36","0","-20","16","0","-4","2","0","0","-16","0","0","40","0","-4","40","0","-4","-24","0","-12","16","0","0","-8","0","-8","-36","0","-22","28","0","16","-32","0","-48","24","0","-16","0","0","20","24","0","20","4","0","-16","-16","0","48","-28","0","32","-44","0","-36","20","0","-16","6","0","40","-64","0","28","16","0","18","-24","0","8","28","0","16","-8","0","-36","80","0","48","-32","0","-32","6","0","16","16","0","52","-24","0","12","-12","0","64","-64","0","-64","-28","0","-20","48","0","-76","0","0","0","-16","0","-12","-16","0","-16","16","0","16","24","0","-32","-76","0","-20","-16","0","-4","52","0","-64","-16","0","-32","-12","0","68","16","0","16","-16","0","4","16","0","0","0","0","-4","-28","0","4","28","0","-14","32","0","24","-20","0","-8","-16","0","8","-8","0","-24","0","0","24","32","0","0","-8","0","-32","16","0","-32","16","0","-32","-54","0","36","-32","0","24","-16","0","8","-28","0","-8","16","0","-24","-16","0","-14","-16","0","-16","16","0","64","16","0","-36","4","0","20","40","0","28","64","0","24","0","0","12","0","0","-64","-4","0","72","-24","0","-8","48","0","-56","-8","0","64","-24","0","-12","52","0","8","-4","0","80","24","0","4","-26","0","32","-32","0","8","52","0","64","-12","0","-16","-16","0","-12","24","0","-32","40","0","-8","24","0","44","-64","0","-72","0","0","16","8","0","48","-12","0","-84","-32","0","-16","64","0","8","80","0","-88","-16","0","-62","12","0","-20","72","0","24","32","0","24","32","0","-2","-8","0","88","-4","0","40","-64","0","16","0","0","-8","-6","0","16","28","0","0","-48","0","-16","72","0","-36","-16","0","28","0","0","-16","-36","0","-16","8","0","-12","-36","0","2","-76","0","32","-80","0","-32","-28","0","16","48","0","24","-4","0","-40","-20","0","72","-64","0","0","-20","0","-48","-44","0","32","-28","0","-56","-32","0","36","16","0","-64","-32","0","0","-40","0","12","-8","0","-32","-22","0","28","-12","0","-32","8","0","-80","48","0","-28","-48","0","-24","16","0","-8","0","0","-16","-4","0","-16","20","0","56","64","0","32","36","0","4","48","0","36","-40","0","-48","-48","0","64","80","0","20","4","0","84","32","0","-76","-40","0","-24","-28","0","-28","-16","0","-8","48","0","6","0","0","-8","64","0","-64","64","0","-4","-20","0","0","-60","0","-88","-18","0","16","24","0","64","16","0","4","-60","0","-32","32","0","24","16","0","32","12","0","144","8","0","64","64","0","-16","52","0","-12","-48","0","14","-4","0","32","32","0","80","4","0","-50","20","0","-24","0","0","0","12","0","36","-16","0","-4","48","0","-32","20","0","-24","-96","0","-44","68","0","32","12","0","80","0","0","-8","-68","0","32","-32","0","28","-48","0","0","-28","0","-24","-28","0","-112","16","0","32","80","0","40","-32","0","64","88","0","-32","16","0","-8","-48","0","-68","0","0","8","-52","0","-16","80","0","8","12","0","84","0","0","-16","-32","0","-24","4","0","-12","-8","0","12","16","0","0","116","0","16","-64","0","-20","-16","0","-64","-40","0","-64","-12","0","48","76","0","-12","24","0","-80","-92","0","-64","-4","0","4","16","0","-14","-12","0","44","64","0","8","-42","0","48","8","0","-64","80","0","12","-56","0","-48","-16","0","48","-28","0","-48","-24","0","-16","32","0","32","16","0","16","32","0","12","-16","0","16"],"lmfdb":"agrees"}],"seconds":0.196,"computed":"atlas","estimate":{"seconds":0.218,"low":0.133,"high":0.378,"bytes":1852130}}