{"label":"332.2.a","level":332,"weight":2,"dims":{"new":7,"cusp":40,"eisenstein":5,"modsym":85},"old":[[83,7,3],[166,6,2]],"T":[[3,1],[5,3]],"status":"proven","checks":["dim M^+ at levels [1, 2, 4, 83, 166, 332]: [0, 1, 2, 8, 23, 45] (certified at ell = 2147483323)","T = [(3, 1), (5, 3)]; h of degree 7 = 1 x 7 (phi(ord eps) x dim S_k^new); 1 primes, 0 rejected"],"newforms":[{"label":"332.2.a.a","letter":"a","dim":2,"charpoly":["-7","2","1"],"traces":["2","0","-2","0","0","0","-6","0","0","0","-6","0","0","0","-4","0","-2","0","-4","0","2","0","0","0","-6","0","-2","0","2","0","-6","0","2","0","4","0","2","0","4","0","0","0","-8","0","8","0","-8","0","8","0","10","0","4","0","4","0","8","0","6","0","14","0","8","0","-4","0","-12","0","24","0","12","0","-12","0","6","0","22","0","-4","0","-2","0","2","0","-8","0","-2","0","24","0","-4","0","2","0","-4","0","-16","0","8","0","-12","0","-24","0","8","0","12","0","2","0","6","0","-18","0","-24","0","-8","0","-2","0","0","0","-8","0","0","0","-14","0","-8","0","32","0","8","0","4","0","4","0","-4","0","-4","0","-4","0","0","0","16","0","16","0","-18","0","-16","0","4","0","8","0","4","0","-24","0","-20","0","8","0","14","0","-22","0","-8","0","-18","0","18","0","-26","0","12","0","-8","0","-22","0","-8","0","-2","0","10","0","-34","0","-24","0","4","0","6","0","32","0","-4","0","-6","0","8","0","-48","0","8","0","-8","0","-36","0","16","0","22","0","8","0","8","0","0","0","0","0","20","0","24","0","2","0","-16","0","12","0","32","0","0","0","-6","0","32","0","-24","0","4","0","-2","0","0","0","-24","0","12","0","-8","0","-14","0","0","0","4","0","-8","0","-16","0","4","0","32","0","-8","0","18","0","32","0","8","0","-44","0","-44","0","12","0","8","0","-16","0","-8","0","24","0","20","0","10","0","24","0","40","0","28","0","8","0","24","0","32","0","0","0","14","0","-24","0","-26","0","-6","0","4","0","12","0","0","0","30","0","36","0","12","0","-16","0","16","0","4","0","-6","0","22","0","-6","0","24","0","36","0","2","0","-4","0","-34","0","24","0","-18","0","18","0","-26","0","24","0","4","0","-12","0","16","0","-20","0","2","0","32","0","0","0","-48","0","-22","0","22","0","-24","0","32","0","-28","0","48","0","-16","0","-28","0","-20","0","-12","0","16","0","-4","0","-24","0","-14","0","14","0","-12","0","2","0","0","0","-48","0","10","0","12","0","24","0","6","0","-34","0","-8","0","-34","0","-32","0","-4","0","24","0","16","0","-48","0","-18","0","-8","0","-40","0","-48","0","8","0","22","0","12","0","-52","0","-6","0","-64","0","-6","0","8","0","-8","0","52","0","12","0","40","0","12","0","-16","0","38","0","8","0","-48","0","24","0","0","0","40","0","-68","0","-2","0","-24","0","-12","0","-46","0","-26","0","32","0","-16","0","22","0","-22","0","40","0","0","0","-8","0","36","0","18","0","-40","0","-38","0","-6","0","-2","0","98","0","40","0","-8","0","-16","0","24","0","-48","0","44","0","-52","0","-32","0","-14","0","16","0","-4","0","-16","0","4","0","-56","0","-16","0","-18","0","-10","0","24","0","-18","0","56","0","0","0","30","0","0","0","28","0","24","0","-6","0","-20","0","0","0","-48","0","8","0","-46","0","-18","0","20","0","-48","0","-8","0","48","0","32","0","-24","0","0","0","2","0","-12","0","52","0","-8","0","46","0","26","0","-24","0","-80","0","-2","0","-12","0","14","0","-24","0","28","0","36","0","24","0","48","0","48","0","24","0","0","0","-84","0","2","0","2","0","56","0","-16","0","8","0","8","0","12","0","-12","0","4","0","0","0","68","0","-34","0","42","0","6","0","68","0","72","0","-36","0","-16","0","8","0","-32","0","8","0","46","0","-48","0","52","0","-16","0","20","0","-68","0","4","0","4","0","20","0","0","0","-56","0","-24","0","12","0","-40","0","24","0","64","0","78","0","-6","0","-6","0","-42","0","-24","0","42","0","8","0","52","0","-28","0","-12","0","0","0","24","0","0","0","-52","0","-16","0","44","0","-4","0","6","0","-48","0","-24","0","-38","0","-8","0","-20","0","76","0","36","0","-16","0","18","0","-14","0","-8","0","-12","0","-2","0","-20","0","16","0","-32","0","78","0","-8","0","0","0","104","0","-16","0","-16","0","40","0","72","0","28","0","20","0","72","0","-72","0","-20","0","0","0","24","0","12","0","-56","0","-6","0","32","0","-20","0","-56","0","40","0","12","0","10","0","50","0","-56","0","48","0","0","0","-24","0","72","0","48","0","30","0","-16","0","-58","0","-62","0","16","0","-14","0","0","0","0","0","-16","0","-16","0","48","0","-32","0","-12","0","8","0","26","0","-60","0","-32","0","-40","0","78","0","-18","0","4","0","-36","0","-24","0","-6","0","12","0","24","0","60","0","-26","0","-32","0","30","0","-6","0","-36","0","-112","0","-16","0","4","0","-24","0","-6","0","-16","0","-70","0","8","0","-32","0","20","0","-28","0","-94","0","-58","0","-48","0","-16","0","16","0","-4","0","26","0","-18","0","4","0","2","0","-4","0","-40","0","-32","0","0","0","12","0","-32","0","20","0","64","0","-12","0","26","0","-80","0","-64","0","-16","0","40","0","16","0","-96","0","-10","0","12","0","16","0","-22","0","-10","0"],"lmfdb":"agrees"},{"label":"332.2.a.b","letter":"b","dim":2,"charpoly":["-103","6","1"],"traces":["2","0","0","0","-2","0","0","0","8","0","4","0","-6","0","14","0","6","0","6","0","-14","0","4","0","6","0","0","0","-6","0","0","0","14","0","-14","0","6","0","-14","0","-24","0","16","0","-8","0","-6","0","0","0","0","0","16","0","10","0","-14","0","0","0","-2","0","0","0","-8","0","28","0","-28","0","16","0","-14","0","-28","0","-14","0","-22","0","-10","0","-2","0","-6","0","0","0","4","0","14","0","-14","0","-20","0","20","0","16","0","12","0","12","0","14","0","4","0","-2","0","28","0","-6","0","-32","0","-24","0","0","0","0","0","0","0","-24","0","16","0","0","0","-8","0","14","0","14","0","32","0","-14","0","42","0","-26","0","6","0","0","0","20","0","4","0","24","0","-14","0","-14","0","-28","0","28","0","30","0","14","0","-12","0","6","0","24","0","18","0","28","0","-42","0","14","0","-6","0","0","0","22","0","12","0","-14","0","0","0","4","0","-28","0","-14","0","16","0","0","0","0","0","24","0","16","0","-2","0","-14","0","-28","0","-16","0","14","0","-42","0","-18","0","42","0","24","0","8","0","0","0","-28","0","-22","0","48","0","14","0","-20","0","34","0","0","0","0","0","-4","0","0","0","-2","0","-20","0","42","0","14","0","-28","0","-24","0","-26","0","-44","0","-28","0","-12","0","-28","0","42","0","-16","0","-56","0","0","0","30","0","34","0","56","0","0","0","-16","0","-28","0","-12","0","-42","0","14","0","16","0","0","0","0","0","2","0","6","0","28","0","-16","0","-2","0","-56","0","-26","0","-12","0","56","0","18","0","10","0","-84","0","-42","0","0","0","24","0","-28","0","48","0","-84","0","-14","0","0","0","56","0","-4","0","-30","0","-14","0","-14","0","-44","0","-42","0","16","0","-6","0","56","0","-28","0","0","0","-96","0","28","0","-30","0","0","0","18","0","36","0","42","0","60","0","-14","0","64","0","22","0","12","0","56","0","36","0","-4","0","-42","0","-12","0","14","0","10","0","40","0","54","0","28","0","42","0","2","0","-42","0","-32","0","0","0","-24","0","18","0","0","0","-70","0","-48","0","-12","0","-42","0","40","0","-30","0","0","0","-12","0","-32","0","28","0","22","0","-48","0","42","0","28","0","8","0","0","0","0","0","36","0","14","0","-18","0","0","0","42","0","32","0","46","0","64","0","36","0","-46","0","-28","0","-48","0","26","0","-14","0","-30","0","-18","0","40","0","28","0","-52","0","42","0","-36","0","-12","0","84","0","-6","0","42","0","-14","0","16","0","30","0","84","0","56","0","-36","0","-42","0","0","0","18","0","0","0","72","0","52","0","-14","0","0","0","-20","0","-14","0","-82","0","-8","0","-8","0","-18","0","-14","0","14","0","0","0","-48","0","42","0","12","0","-78","0","0","0","-30","0","8","0","-42","0","68","0","12","0","84","0","0","0","4","0","-32","0","-26","0","14","0","-28","0","14","0","-42","0","0","0","30","0","-10","0","112","0","56","0","-20","0","42","0","-24","0","-74","0","-168","0","-66","0","12","0","-28","0","28","0","-6","0","14","0","18","0","-12","0","42","0","26","0","0","0","64","0","24","0","-74","0","112","0","-76","0","-42","0","0","0","8","0","64","0","-56","0","32","0","10","0","-42","0","-56","0","-12","0","-14","0","-4","0","-46","0","-28","0","54","0","28","0","28","0","-26","0","-4","0","112","0","-20","0","0","0","-56","0","-28","0","-72","0","-14","0","20","0","-10","0","-84","0","0","0","-30","0","-88","0","28","0","-44","0","-28","0","-12","0","-28","0","0","0","-18","0","-8","0","-82","0","48","0","-6","0","0","0","56","0","64","0","0","0","-16","0","8","0","-8","0","-56","0","12","0","14","0","38","0","-46","0","-28","0","16","0","84","0","-24","0","42","0","22","0","-98","0","8","0","28","0","-42","0","-72","0","4","0","0","0","56","0","12","0","-70","0","84","0","6","0","140","0","-32","0","-18","0","16","0","-70","0","-56","0","0","0","-38","0","4","0","-28","0","-44","0","48","0","56","0","90","0","-18","0","-14","0","-26","0","-32","0","0","0","0","0","54","0","-14","0","-4","0","-40","0","42","0","78","0","-56","0","-42","0","-44","0","58","0","-80","0","2","0","12","0","168","0","104","0","66","0","0","0","-30","0","-84","0","80","0","0","0","-60","0","84","0","38","0","64","0","42","0","-78","0","-42","0","-20","0","-60","0","-28","0","56","0","0","0","48","0","-112","0","-8","0","-40","0","48","0","40","0","-4","0","-14","0","-56","0","16","0","-98","0","-20","0","-38","0","48","0","-30","0","0","0","112","0","30","0","18","0","0","0","-22","0","-48","0","14","0","-36","0","84","0","56","0","-22","0","-42","0","-42","0","-28","0","-48","0","16","0","80","0","48","0","-42","0","78","0","42","0","42","0","-34","0","-20","0","-8","0","-12","0","-14","0","42","0","32","0","-4","0","28","0","-16","0","26","0","28","0"],"lmfdb":"agrees"},{"label":"332.2.a.c","letter":"c","dim":3,"charpoly":["139","-39","-10","1"],"traces":["3","0","4","0","2","0","8","0","1","0","-4","0","6","0","-2","0","-4","0","4","0","13","0","1","0","5","0","1","0","-8","0","8","0","-17","0","10","0","-16","0","8","0","5","0","0","0","-18","0","2","0","5","0","-3","0","-24","0","-12","0","10","0","4","0","0","0","5","0","-24","0","6","0","-8","0","0","0","12","0","16","0","-27","0","12","0","3","0","-3","0","-26","0","-20","0","-2","0","2","0","-15","0","-16","0","-22","0","-20","0","2","0","4","0","4","0","-2","0","-16","0","-33","0","4","0","38","0","16","0","-20","0","33","0","16","0","12","0","36","0","-14","0","3","0","6","0","-32","0","2","0","8","0","26","0","34","0","18","0","16","0","-52","0","20","0","15","0","52","0","18","0","-32","0","12","0","14","0","-16","0","-4","0","29","0","20","0","-24","0","32","0","17","0","-12","0","34","0","28","0","8","0","31","0","-9","0","0","0","31","0","-60","0","20","0","-23","0","36","0","-19","0","-34","0","-37","0","4","0","10","0","14","0","0","0","19","0","2","0","34","0","20","0","11","0","-32","0","-21","0","-57","0","28","0","-36","0","2","0","-30","0","-4","0","-13","0","36","0","36","0","-4","0","-22","0","-20","0","-44","0","10","0","-45","0","-33","0","-18","0","12","0","44","0","4","0","46","0","12","0","-72","0","5","0","-72","0","40","0","-52","0","-40","0","4","0","-13","0","-48","0","13","0","26","0","29","0","-54","0","-14","0","26","0","-14","0","44","0","-18","0","-8","0","12","0","-48","0","-16","0","13","0","2","0","18","0","-46","0","-33","0","10","0","-8","0","-38","0","32","0","24","0","-4","0","22","0","-17","0","74","0","16","0","-28","0","58","0","44","0","28","0","-22","0","-20","0","-33","0","23","0","36","0","24","0","39","0","-50","0","-36","0","44","0","-44","0","-38","0","62","0","0","0","-74","0","-28","0","24","0","-48","0","4","0","8","0","-75","0","22","0","-3","0","-26","0","-12","0","40","0","-64","0","-16","0","34","0","-2","0","-22","0","-68","0","34","0","66","0","-44","0","21","0","-6","0","40","0","6","0","52","0","-36","0","20","0","4","0","64","0","-76","0","-60","0","-10","0","12","0","78","0","-92","0","-34","0","43","0","-6","0","48","0","88","0","56","0","58","0","-32","0","56","0","-12","0","-22","0","72","0","-46","0","-5","0","4","0","72","0","28","0","22","0","-15","0","38","0","28","0","12","0","46","0","76","0","20","0","48","0","-48","0","32","0","34","0","40","0","-40","0","-53","0","11","0","-40","0","59","0","-55","0","6","0","13","0","66","0","-20","0","-44","0","-93","0","-12","0","78","0","-6","0","-4","0","63","0","-34","0","18","0","48","0","38","0","28","0","39","0","-48","0","-58","0","-13","0","8","0","-10","0","49","0","39","0","6","0","32","0","-8","0","-10","0","-64","0","42","0","-36","0","-13","0","-60","0","-102","0","-40","0","-56","0","18","0","44","0","120","0","3","0","-51","0","32","0","-22","0","-78","0","16","0","48","0","-65","0","4","0","-17","0","-18","0","5","0","14","0","32","0","10","0","-74","0","14","0","34","0","26","0","0","0","-28","0","-87","0","-19","0","-14","0","2","0","-38","0","-64","0","-6","0","64","0","-52","0","44","0","78","0","-91","0","84","0","-45","0","18","0","-68","0","-80","0","58","0","-64","0","0","0","-104","0","-72","0","-23","0","24","0","40","0","28","0","-37","0","-40","0","-76","0","38","0","-60","0","-24","0","96","0","144","0","-68","0","84","0","6","0","-59","0","-4","0","-16","0","-38","0","14","0","20","0","62","0","-162","0","-29","0","76","0","-34","0","-72","0","-1","0","-10","0","-72","0","8","0","-38","0","-16","0","-15","0","-80","0","-52","0","-4","0","-62","0","-56","0","46","0","-6","0","4","0","-95","0","44","0","-98","0","-40","0","152","0","31","0","-10","0","-29","0","-28","0","72","0","48","0","30","0","130","0","-2","0","134","0","38","0","-24","0","-28","0","66","0","-56","0","0","0","66","0","62","0","10","0","-75","0","70","0","56","0","44","0","-65","0","-54","0","-65","0","36","0","-33","0","100","0","-18","0","116","0","-74","0","32","0","-36","0","-52","0","84","0","-76","0","31","0","40","0","40","0","-8","0","40","0","-100","0","-54","0","60","0","-56","0","8","0","20","0","18","0","44","0","28","0","103","0","73","0","40","0","-36","0","-128","0","51","0","-10","0","-42","0","4","0","72","0","38","0","104","0","4","0","-28","0","8","0","60","0","96","0","-84","0","-36","0","-64","0","24","0","-26","0","-6","0","142","0","-6","0","-61","0","-8","0","-73","0","-118","0","-10","0","-4","0","-5","0","-24","0","-70","0","50","0","-46","0","101","0","18","0","58","0","26","0","38","0","58","0","-2","0","-24","0","36","0","-72","0","-31","0","8","0","18","0","60","0","0","0","-44","0","-34","0","-34","0","16","0","-31","0"],"lmfdb":"agrees"}],"seconds":0.186,"computed":"atlas","estimate":{"seconds":0.288,"low":0.176,"high":0.499,"bytes":1922299}}