{"label":"232.2.a","level":232,"weight":2,"dims":{"new":7,"cusp":27,"eisenstein":7,"modsym":61},"old":[[29,2,4],[58,2,3],[116,3,2]],"T":[[3,1],[5,1]],"status":"proven","checks":["dim M^+ at levels [1, 2, 4, 8, 29, 58, 116, 232]: [0, 1, 2, 3, 3, 9, 18, 34] (certified at ell = 2147483549)","T = [(3, 1), (5, 1)]; h of degree 7 = 1 x 7 (phi(ord eps) x dim S_k^new); 1 primes, 0 rejected"],"newforms":[{"label":"232.2.a.a","letter":"a","dim":1,"charpoly":["4","1"],"traces":["1","0","-1","0","-3","0","2","0","-2","0","-3","0","-5","0","3","0","-4","0","0","0","-2","0","0","0","4","0","5","0","-1","0","9","0","3","0","-6","0","8","0","5","0","-2","0","-11","0","6","0","-7","0","-3","0","4","0","9","0","9","0","0","0","4","0","-12","0","-4","0","15","0","12","0","0","0","2","0","-4","0","-4","0","-6","0","3","0","1","0","-16","0","12","0","1","0","2","0","-10","0","-9","0","0","0","-14","0","6","0","0","0","-10","0","6","0","-14","0","1","0","-8","0","-6","0","0","0","10","0","-8","0","-2","0","2","0","3","0","16","0","11","0","-4","0","0","0","-15","0","-12","0","8","0","7","0","15","0","3","0","3","0","11","0","-2","0","8","0","-27","0","-18","0","-9","0","0","0","-15","0","-9","0","-18","0","12","0","0","0","-14","0","8","0","-4","0","22","0","19","0","12","0","-24","0","12","0","10","0","24","0","2","0","-15","0","-14","0","26","0","-12","0","-2","0","6","0","0","0","0","0","-3","0","-2","0","33","0","18","0","4","0","20","0","-2","0","-8","0","18","0","-26","0","6","0","-9","0","21","0","-3","0","20","0","1","0","-16","0","9","0","0","0","16","0","3","0","0","0","-12","0","29","0","16","0","2","0","-19","0","-27","0","-2","0","-12","0","-25","0","10","0","-12","0","-2","0","-18","0","-29","0","24","0","0","0","-4","0","-1","0","14","0","6","0","-12","0","-15","0","0","0","-22","0","0","0","36","0","-7","0","10","0","-24","0","-15","0","12","0","8","0","3","0","14","0","0","0","-20","0","-1","0","-14","0","17","0","-16","0","-36","0","-12","0","6","0","-27","0","-20","0","0","0","30","0","21","0","-25","0","30","0","-6","0","8","0","3","0","-19","0","2","0","12","0","-8","0","4","0","18","0","15","0","-3","0","5","0","-28","0","-16","0","-6","0","18","0","22","0","24","0","0","0","4","0","-9","0","-13","0","0","0","11","0","-45","0","-3","0","-24","0","-18","0","12","0","8","0","48","0","-8","0","6","0","-20","0","14","0","-16","0","-24","0","-15","0","-12","0","8","0","-3","0","0","0","-8","0","6","0","12","0","-6","0","-11","0","6","0","6","0","2","0","30","0","38","0","-20","0","10","0","-24","0","27","0","21","0","24","0","18","0","33","0","0","0","-18","0","-17","0","-40","0","0","0","42","0","14","0","15","0","15","0","4","0","-18","0","4","0","-16","0","18","0","-9","0","0","0","-12","0","29","0","-8","0","0","0","30","0","21","0","14","0","-29","0","16","0","-8","0","-36","0","-23","0","-8","0","10","0","42","0","-22","0","9","0","-8","0","-19","0","-3","0","-22","0","24","0","0","0","6","0","24","0","-34","0","55","0","-12","0","13","0","18","0","2","0","26","0","-20","0","-24","0","0","0","28","0","-2","0","-32","0","-27","0","-30","0","32","0","0","0","14","0","-25","0","24","0","-26","0","-1","0","22","0","-24","0","6","0","-9","0","2","0","35","0","37","0","-6","0","-28","0","5","0","0","0","4","0","-29","0","0","0","-32","0","18","0","3","0","-48","0","15","0","-4","0","28","0","-34","0","-33","0","12","0","-12","0","-18","0","-6","0","12","0","8","0","-25","0","14","0","-20","0","0","0","0","0","2","0","36","0","1","0","20","0","30","0","-28","0","-18","0","-8","0","36","0","26","0","-45","0","-4","0","12","0","-24","0","8","0","9","0","7","0","0","0","-21","0","0","0","-37","0","-6","0","0","0","-45","0","-20","0","-26","0","-20","0","-1","0","-4","0","-8","0","13","0","44","0","-24","0","-9","0","-36","0","-37","0","0","0","20","0","-33","0","32","0","-28","0","40","0","-3","0","6","0","-20","0","0","0","50","0","2","0","-24","0","-20","0","-32","0","-29","0","-14","0","36","0","-16","0","0","0","-6","0","-5","0","54","0","-30","0","19","0","-12","0","60","0","27","0","-20","0","28","0","-4","0","12","0","0","0","12","0","8","0","2","0","25","0","45","0","0","0","20","0","-45","0","40","0","12","0","45","0","28","0","2","0","12","0","54","0","45","0","17","0","1","0","29","0","-36","0","-4","0","-24","0","0","0","-2","0","0","0","-3","0","-41","0","4","0","-46","0","42","0","1","0","-9","0","-60","0","28","0","6","0","17","0","-6","0","18","0","-22","0","12","0","-3","0","32","0","-3","0","0","0","-66","0","0","0","-9","0","-36","0","22","0","-57","0","-44","0","0","0","39","0","48","0","-36","0","-8","0","54","0","7","0","-10","0","32","0","20","0","-14","0","0","0","24","0","-36","0","30","0","15","0","33","0","0","0","-30","0","9","0","20","0","-8","0","-33","0","-72","0","-3","0","-24","0","50","0","28","0","-6","0","-23","0","0","0","-20","0","16","0","20","0","-3","0","-6","0","-2","0","-3","0","42","0","14","0","0","0","46","0","-17","0","-78","0","8","0","40","0"],"lmfdb":"agrees","curve":{"cremona":"232a1","lmfdb":"232.a","ainvs":[0,-1,0,8,-4],"rank":1,"torsion":1},"derived":{"al":[[2,null],[29,1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"232.2.a.b","letter":"b","dim":1,"charpoly":["-2","1"],"traces":["1","0","1","0","1","0","2","0","-2","0","3","0","-1","0","1","0","0","0","0","0","2","0","4","0","-4","0","-5","0","-1","0","3","0","3","0","2","0","-8","0","-1","0","-6","0","-5","0","-2","0","3","0","-3","0","0","0","5","0","3","0","0","0","-8","0","0","0","-4","0","-1","0","-12","0","4","0","6","0","-4","0","-4","0","6","0","1","0","1","0","-12","0","0","0","-1","0","6","0","-2","0","3","0","0","0","14","0","-6","0","16","0","10","0","2","0","18","0","-11","0","-8","0","18","0","4","0","2","0","0","0","-2","0","-6","0","-9","0","8","0","-5","0","4","0","0","0","-5","0","12","0","4","0","3","0","-3","0","-1","0","-3","0","-1","0","22","0","0","0","3","0","-14","0","5","0","8","0","-9","0","3","0","2","0","-12","0","0","0","10","0","-8","0","-8","0","-6","0","-25","0","0","0","-8","0","0","0","-10","0","-8","0","14","0","-1","0","2","0","-14","0","-12","0","-2","0","-6","0","-8","0","0","0","3","0","6","0","-5","0","6","0","-4","0","0","0","26","0","8","0","6","0","10","0","6","0","-17","0","3","0","1","0","-16","0","-31","0","16","0","-3","0","0","0","-12","0","21","0","12","0","0","0","-3","0","-16","0","2","0","-25","0","5","0","6","0","-24","0","29","0","-2","0","-12","0","14","0","-6","0","-5","0","12","0","0","0","-12","0","-17","0","14","0","22","0","-8","0","-15","0","-4","0","-10","0","16","0","0","0","23","0","10","0","8","0","9","0","-4","0","-28","0","-3","0","18","0","0","0","4","0","-11","0","6","0","7","0","16","0","-12","0","24","0","18","0","9","0","-20","0","4","0","10","0","1","0","5","0","22","0","6","0","0","0","25","0","-19","0","-2","0","-4","0","-16","0","12","0","10","0","27","0","-9","0","1","0","-20","0","8","0","26","0","6","0","10","0","-24","0","0","0","4","0","1","0","-1","0","0","0","-5","0","-3","0","1","0","-24","0","22","0","12","0","-16","0","-12","0","4","0","-22","0","16","0","-6","0","0","0","0","0","-3","0","-40","0","-8","0","-1","0","0","0","20","0","6","0","-20","0","6","0","-1","0","22","0","-18","0","22","0","-2","0","-34","0","0","0","-6","0","12","0","3","0","27","0","-24","0","-14","0","-15","0","0","0","-10","0","-27","0","8","0","8","0","14","0","-26","0","-9","0","-15","0","0","0","-6","0","12","0","4","0","2","0","-19","0","16","0","-12","0","1","0","-8","0","0","0","10","0","9","0","10","0","-45","0","-24","0","-8","0","0","0","-7","0","16","0","6","0","18","0","-6","0","-9","0","8","0","-25","0","-11","0","-14","0","0","0","0","0","2","0","-8","0","-18","0","5","0","0","0","27","0","18","0","2","0","26","0","20","0","-8","0","-16","0","-8","0","14","0","-24","0","15","0","2","0","12","0","0","0","2","0","7","0","0","0","-14","0","-27","0","26","0","24","0","-2","0","45","0","-2","0","-3","0","1","0","-6","0","-4","0","35","0","-20","0","12","0","11","0","0","0","0","0","6","0","3","0","8","0","3","0","-12","0","-24","0","-2","0","-5","0","32","0","-24","0","6","0","-10","0","4","0","8","0","1","0","-18","0","0","0","0","0","-4","0","26","0","0","0","9","0","20","0","22","0","28","0","6","0","-16","0","12","0","10","0","-5","0","-20","0","-12","0","4","0","0","0","-17","0","-5","0","0","0","3","0","32","0","-33","0","-2","0","12","0","-3","0","-16","0","42","0","20","0","-31","0","4","0","8","0","13","0","0","0","0","0","-3","0","-36","0","-43","0","0","0","-12","0","-1","0","24","0","36","0","32","0","21","0","22","0","8","0","12","0","10","0","-22","0","0","0","8","0","20","0","-3","0","-18","0","-12","0","-16","0","0","0","18","0","5","0","-14","0","-18","0","-25","0","36","0","0","0","5","0","24","0","0","0","-12","0","-12","0","8","0","-24","0","-32","0","-6","0","29","0","-9","0","0","0","4","0","15","0","-16","0","-12","0","35","0","-40","0","14","0","0","0","2","0","-15","0","35","0","1","0","-5","0","-12","0","-4","0","12","0","-32","0","-2","0","0","0","21","0","-55","0","-12","0","-18","0","10","0","-17","0","3","0","12","0","-28","0","-18","0","29","0","22","0","-30","0","-38","0","-8","0","15","0","16","0","3","0","0","0","-6","0","-4","0","-3","0","0","0","-10","0","-25","0","-44","0","-32","0","13","0","-36","0","0","0","8","0","-6","0","23","0","-6","0","32","0","-20","0","34","0","0","0","8","0","0","0","-18","0","9","0","5","0","-24","0","-10","0","15","0","4","0","-28","0","47","0","-8","0","-3","0","24","0","-22","0","-36","0","14","0","-29","0","0","0","-36","0","8","0","4","0","-35","0","18","0","22","0","-1","0","2","0","6","0","-20","0","-38","0","7","0","-14","0","-32","0","40","0"],"lmfdb":"agrees","curve":{"cremona":"232b1","lmfdb":"232.b","ainvs":[0,1,0,-80,-304],"rank":0,"torsion":1},"derived":{"al":[[2,null],[29,1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"232.2.a.c","letter":"c","dim":2,"charpoly":["2","4","1"],"traces":["2","0","-2","0","-2","0","-8","0","0","0","-2","0","-2","0","-6","0","-4","0","4","0","8","0","-4","0","8","0","-2","0","2","0","-14","0","-2","0","8","0","8","0","18","0","-8","0","6","0","16","0","-10","0","18","0","20","0","-14","0","10","0","-4","0","4","0","12","0","0","0","-30","0","0","0","-4","0","-4","0","8","0","8","0","8","0","-6","0","-2","0","-12","0","-28","0","-2","0","-8","0","8","0","10","0","-4","0","8","0","8","0","0","0","-28","0","24","0","16","0","-2","0","-24","0","-20","0","20","0","-32","0","16","0","-16","0","-8","0","-30","0","20","0","-10","0","-20","0","-16","0","10","0","24","0","12","0","-10","0","-14","0","-2","0","-18","0","6","0","24","0","-32","0","22","0","0","0","14","0","16","0","-6","0","2","0","-20","0","40","0","0","0","-28","0","-32","0","20","0","28","0","-6","0","-12","0","24","0","-12","0","8","0","4","0","0","0","22","0","4","0","-40","0","-16","0","-8","0","40","0","16","0","-4","0","-46","0","28","0","2","0","56","0","-8","0","68","0","28","0","-32","0","-28","0","24","0","8","0","-2","0","50","0","42","0","-12","0","-14","0","32","0","-18","0","-4","0","4","0","6","0","12","0","28","0","-10","0","-32","0","0","0","10","0","14","0","-8","0","12","0","-10","0","-72","0","-24","0","-12","0","8","0","-2","0","12","0","-12","0","32","0","38","0","-40","0","-44","0","-52","0","6","0","-28","0","-24","0","32","0","-12","0","-34","0","20","0","4","0","-34","0","-64","0","-28","0","-2","0","-32","0","-8","0","56","0","10","0","40","0","2","0","32","0","32","0","4","0","20","0","18","0","-16","0","4","0","-4","0","-14","0","-14","0","-28","0","-44","0","-80","0","50","0","-30","0","24","0","-8","0","-20","0","32","0","56","0","-14","0","22","0","-2","0","28","0","-4","0","16","0","-40","0","8","0","-24","0","-24","0","20","0","-66","0","-14","0","16","0","6","0","-2","0","-46","0","8","0","12","0","-40","0","-16","0","28","0","-4","0","36","0","-36","0","40","0","48","0","-48","0","2","0","12","0","-16","0","-6","0","-8","0","-12","0","0","0","28","0","40","0","10","0","12","0","24","0","-40","0","120","0","-12","0","-12","0","60","0","12","0","38","0","-10","0","0","0","-32","0","-2","0","16","0","0","0","-18","0","-72","0","16","0","56","0","0","0","34","0","-14","0","-4","0","-24","0","16","0","52","0","44","0","14","0","-64","0","-72","0","26","0","-32","0","-4","0","44","0","30","0","28","0","82","0","48","0","-32","0","12","0","-22","0","-48","0","-56","0","16","0","-52","0","-18","0","16","0","30","0","-14","0","40","0","0","0","4","0","24","0","-40","0","4","0","-22","0","4","0","-22","0","20","0","8","0","28","0","16","0","-20","0","-48","0","44","0","16","0","48","0","14","0","16","0","4","0","-28","0","28","0","-6","0","112","0","24","0","-22","0","-24","0","32","0","0","0","-2","0","8","0","-70","0","-2","0","8","0","-40","0","-6","0","12","0","32","0","6","0","-4","0","-80","0","-12","0","58","0","-52","0","-18","0","-48","0","-52","0","-40","0","-22","0","4","0","-28","0","-40","0","48","0","20","0","0","0","-10","0","-36","0","-116","0","16","0","-4","0","12","0","-12","0","-14","0","-24","0","-12","0","-32","0","36","0","-24","0","8","0","-8","0","14","0","-16","0","-32","0","-28","0","-48","0","18","0","30","0","16","0","10","0","0","0","-2","0","-72","0","36","0","38","0","52","0","-52","0","112","0","-18","0","8","0","20","0","-42","0","-28","0","-40","0","-54","0","16","0","-26","0","36","0","-20","0","-38","0","16","0","-64","0","20","0","-66","0","8","0","52","0","4","0","-36","0","8","0","0","0","92","0","12","0","2","0","40","0","-72","0","96","0","-16","0","-20","0","-2","0","64","0","12","0","-62","0","80","0","-12","0","42","0","12","0","-60","0","32","0","-8","0","-80","0","36","0","0","0","88","0","14","0","-50","0","12","0","128","0","-2","0","-12","0","-8","0","-62","0","44","0","-52","0","-36","0","-28","0","18","0","-10","0","2","0","2","0","24","0","64","0","-20","0","16","0","36","0","32","0","-18","0","34","0","32","0","-36","0","28","0","-102","0","-30","0","-64","0","64","0","120","0","34","0","76","0","44","0","32","0","12","0","-14","0","-80","0","-22","0","-20","0","20","0","4","0","-14","0","28","0","40","0","-42","0","12","0","-64","0","54","0","20","0","-36","0","80","0","12","0","-2","0","100","0","-32","0","16","0","-36","0","36","0","44","0","28","0","-4","0","10","0","14","0","48","0","-40","0","-42","0","-8","0","28","0","-74","0","28","0","-2","0","-96","0","40","0","32","0","-32","0","-42","0","40","0","-44","0","-48","0","-8","0","-34","0","24","0","-16","0","-50","0","-68","0","40","0","-4","0","-60","0","-22","0","72","0","-16","0","8","0"],"lmfdb":"agrees","derived":{"al":[[2,null],[29,-1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"232.2.a.d","letter":"d","dim":3,"charpoly":["4","2","-6","1"],"traces":["3","0","2","0","4","0","0","0","5","0","2","0","4","0","-2","0","6","0","-4","0","0","0","-4","0","7","0","2","0","3","0","-14","0","-2","0","0","0","-2","0","-18","0","10","0","-6","0","-10","0","-2","0","-21","0","4","0","0","0","-26","0","-12","0","8","0","2","0","0","0","-2","0","20","0","-28","0","12","0","2","0","16","0","0","0","-30","0","-17","0","32","0","8","0","2","0","10","0","0","0","-22","0","28","0","-14","0","32","0","6","0","-4","0","0","0","12","0","-4","0","8","0","-2","0","4","0","14","0","0","0","29","0","48","0","30","0","-8","0","-26","0","28","0","0","0","-26","0","2","0","0","0","46","0","38","0","4","0","-14","0","-12","0","-24","0","10","0","-14","0","22","0","-30","0","0","0","-18","0","-62","0","12","0","15","0","-40","0","2","0","0","0","-20","0","-24","0","16","0","52","0","-36","0","4","0","0","0","-8","0","-6","0","-38","0","-22","0","-48","0","64","0","0","0","28","0","-16","0","-60","0","22","0","-36","0","30","0","0","0","-40","0","8","0","-4","0","-29","0","-8","0","6","0","0","0","40","0","-50","0","2","0","28","0","36","0","8","0","-28","0","-20","0","-4","0","-30","0","4","0","-4","0","48","0","0","0","5","0","18","0","26","0","-16","0","18","0","-42","0","0","0","-88","0","10","0","-28","0","-56","0","40","0","60","0","0","0","-39","0","0","0","-22","0","20","0","62","0","36","0","0","0","64","0","-16","0","10","0","-28","0","-48","0","16","0","0","0","26","0","2","0","40","0","-8","0","-54","0","62","0","0","0","30","0","30","0","8","0","46","0","-20","0","-6","0","0","0","-4","0","-16","0","40","0","38","0","-26","0","92","0","0","0","2","0","15","0","56","0","-12","0","-48","0","2","0","0","0","40","0","98","0","4","0","-4","0","36","0","56","0","0","0","-48","0","-66","0","-8","0","28","0","-78","0","-48","0","0","0","8","0","2","0","-32","0","56","0","-42","0","-8","0","0","0","52","0","-76","0","-16","0","10","0","44","0","14","0","0","0","-22","0","-28","0","-14","0","-2","0","24","0","-20","0","-35","0","-12","0","-68","0","54","0","-18","0","-64","0","16","0","0","0","-34","0","4","0","-6","0","44","0","6","0","-30","0","0","0","24","0","-58","0","72","0","-26","0","-34","0","12","0","0","0","-52","0","8","0","58","0","-26","0","6","0","0","0","0","0","-56","0","-36","0","-26","0","-44","0","-112","0","16","0","0","0","-60","0","4","0","46","0","20","0","4","0","20","0","0","0","-28","0","-13","0","4","0","-84","0","64","0","28","0","-14","0","30","0","-54","0","-74","0","-4","0","22","0","-4","0","0","0","-56","0","18","0","-2","0","-4","0","62","0","64","0","0","0","6","0","20","0","-28","0","-32","0","-42","0","56","0","0","0","-22","0","28","0","-24","0","28","0","4","0","36","0","0","0","0","0","-54","0","58","0","52","0","70","0","46","0","0","0","-50","0","-60","0","64","0","50","0","22","0","4","0","0","0","51","0","-116","0","-4","0","-28","0","34","0","4","0","-28","0","-56","0","-10","0","100","0","58","0","28","0","12","0","0","0","38","0","4","0","18","0","10","0","50","0","-36","0","0","0","-4","0","60","0","-12","0","-44","0","-88","0","42","0","0","0","84","0","-36","0","36","0","64","0","34","0","12","0","0","0","28","0","20","0","38","0","4","0","-64","0","-46","0","0","0","12","0","-12","0","44","0","98","0","44","0","-20","0","0","0","-38","0","7","0","-48","0","-13","0","-12","0","38","0","14","0","0","0","-6","0","-4","0","-48","0","6","0","44","0","0","0","-16","0","-26","0","16","0","-46","0","-76","0","-10","0","0","0","-20","0","52","0","6","0","78","0","38","0","-44","0","0","0","16","0","-100","0","2","0","-4","0","-8","0","50","0","0","0","-80","0","22","0","50","0","-4","0","98","0","72","0","0","0","-108","0","58","0","44","0","-34","0","10","0","84","0","0","0","-36","0","48","0","-104","0","14","0","-110","0","-76","0","-42","0","92","0","-6","0","70","0","3","0","-58","0","50","0","0","0","20","0","-16","0","-86","0","32","0","32","0","38","0","0","0","-60","0","-64","0","-26","0","34","0","-56","0","10","0","0","0","-120","0","4","0","-34","0","-4","0","-12","0","-54","0","0","0","-18","0","-92","0","-108","0","-52","0","-14","0","0","0","0","0","90","0","4","0","62","0","6","0","28","0","12","0","0","0","-28","0","-98","0","28","0","-86","0","-16","0","-18","0","28","0","-92","0","-52","0","-74","0","6","0","-20","0","-96","0","0","0","82","0","100","0","-52","0","16","0","-92","0","-2","0","0","0","-15","0","-28","0","-60","0","22","0","-24","0","-60","0","0","0","-8","0","24","0","192","0","62","0","62","0","-96","0","0","0","52","0","12","0","-62","0","-16","0","54","0","56","0"],"lmfdb":"agrees","derived":{"al":[[2,null],[29,-1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.276,"computed":"atlas","estimate":{"seconds":0.279,"low":0.17,"high":0.483,"bytes":1899642},"url":"https://sagebrush.space/atlas/mf/232.2.a"}