{"label":"308.2.a","level":308,"weight":2,"dims":{"new":6,"cusp":43,"eisenstein":11,"modsym":97},"old":[[11,1,6],[14,1,4],[44,1,2],[77,5,3],[154,5,2]],"T":[[3,1],[5,2],[13,3],[17,4],[19,5],[23,6],[29,7],[31,8]],"status":"proven","checks":["dim M^+ at levels [1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308]: [0, 1, 2, 1, 2, 4, 5, 7, 9, 10, 28, 54] (certified at ell = 2147482951)","T = [(3, 1), (5, 2), (13, 3), (17, 4), (19, 5), (23, 6), (29, 7), (31, 8)]; h of degree 6 = 1 x 6 (phi(ord eps) x dim S_k^new); 2 primes, 0 rejected"],"newforms":[{"label":"308.2.a.a","letter":"a","dim":1,"charpoly":["37","1"],"traces":["1","0","-1","0","-1","0","-1","0","-2","0","1","0","-4","0","1","0","-6","0","-2","0","1","0","1","0","-4","0","5","0","2","0","-1","0","-1","0","1","0","-9","0","4","0","6","0","8","0","2","0","-8","0","1","0","6","0","10","0","-1","0","2","0","1","0","-2","0","2","0","4","0","11","0","-1","0","11","0","-14","0","4","0","-1","0","-14","0","1","0","4","0","6","0","-2","0","13","0","4","0","1","0","2","0","-9","0","-2","0","-12","0","-4","0","-1","0","-6","0","4","0","9","0","-11","0","-1","0","8","0","6","0","1","0","-6","0","9","0","-10","0","-8","0","-10","0","2","0","-5","0","-3","0","2","0","8","0","-4","0","-2","0","-1","0","-14","0","-14","0","12","0","1","0","-17","0","-10","0","-1","0","12","0","1","0","-14","0","3","0","4","0","16","0","4","0","-1","0","15","0","5","0","2","0","9","0","-6","0","-5","0","-1","0","-18","0","-4","0","-6","0","-8","0","-11","0","-2","0","-6","0","-2","0","-2","0","2","0","-11","0","-8","0","1","0","14","0","24","0","-17","0","8","0","-4","0","-7","0","1","0","6","0","8","0","14","0","-20","0","20","0","-16","0","-1","0","8","0","-4","0","25","0","1","0","-6","0","26","0","9","0","-4","0","6","0","-10","0","-13","0","14","0","32","0","-4","0","-4","0","-24","0","2","0","12","0","0","0","-2","0","-6","0","19","0","9","0","-6","0","-1","0","5","0","-4","0","-8","0","12","0","2","0","-20","0","4","0","24","0","21","0","-2","0","-3","0","2","0","6","0","12","0","16","0","-4","0","8","0","25","0","18","0","-11","0","14","0","11","0","-1","0","-1","0","1","0","-30","0","14","0","-20","0","5","0","-11","0","-6","0","-24","0","-15","0","-1","0","14","0","3","0","-12","0","-10","0","-4","0","-9","0","-8","0","5","0","10","0","-25","0","1","0","-16","0","-27","0","-6","0","10","0","14","0","18","0","-2","0","-38","0","4","0","-1","0","-9","0","14","0","3","0","-1","0","-4","0","-2","0","-24","0","-26","0","16","0","24","0","2","0","4","0","20","0","-37","0","2","0","-2","0","-34","0","-2","0","31","0","-13","0","14","0","-9","0","6","0","14","0","-4","0","-8","0","-30","0","2","0","-33","0","-1","0","-7","0","-11","0","17","0","8","0","8","0","-20","0","12","0","36","0","1","0","9","0","33","0","-12","0","-34","0","-12","0","2","0","-11","0","20","0","14","0","0","0","12","0","-3","0","-31","0","14","0","-10","0","4","0","-8","0","-16","0","3","0","16","0","-4","0","6","0","-22","0","-2","0","-24","0","6","0","-15","0","1","0","16","0","-5","0","-4","0","40","0","4","0","-4","0","14","0","-9","0","-42","0","-32","0","6","0","12","0","11","0","-1","0","14","0","20","0","1","0","-4","0","3","0","18","0","-4","0","10","0","-8","0","36","0","2","0","6","0","-42","0","-6","0","8","0","-24","0","-24","0","-22","0","-1","0","42","0","2","0","32","0","-16","0","6","0","2","0","43","0","5","0","-13","0","11","0","2","0","54","0","41","0","-2","0","10","0","-4","0","-22","0","-9","0","1","0","8","0","21","0","1","0","-1","0","-29","0","10","0","28","0","-46","0","-5","0","-24","0","-2","0","2","0","17","0","-2","0","20","0","-20","0","6","0","9","0","4","0","36","0","3","0","7","0","-40","0","-3","0","2","0","-2","0","-36","0","-6","0","0","0","18","0","-8","0","12","0","35","0","28","0","-1","0","4","0","20","0","27","0","4","0","-20","0","-8","0","-5","0","13","0","-48","0","28","0","1","0","11","0","2","0","-8","0","-8","0","14","0","-8","0","6","0","35","0","-25","0","14","0","-42","0","-1","0","48","0","-4","0","-12","0","-4","0","-8","0","-26","0","26","0","4","0","-9","0","-12","0","11","0","10","0","17","0","-34","0","-6","0","11","0","8","0","10","0","47","0","48","0","-26","0","-14","0","1","0","-14","0","14","0","-34","0","-32","0","-12","0","-16","0","-8","0","-38","0","29","0","4","0","28","0","-5","0","24","0","-6","0","14","0","-5","0","27","0","-25","0","-12","0","-3","0","-1","0","0","0","-9","0","-2","0","-4","0","-12","0","-43","0","6","0","4","0","-16","0","-19","0","-14","0","-44","0","18","0","-9","0","-46","0","6","0","-33","0","-4","0","1","0","2","0","10","0","1","0","16","0","-15","0","4","0","-2","0","-60","0","8","0","-5","0","-24","0","24","0","8","0","4","0","-2","0","10","0","16","0","20","0","-44","0","36","0","8","0","-46","0","-2","0","-24","0","6","0","-28","0","-21","0","42","0","6","0","5","0","-45","0","56","0","3","0","28","0","1","0","-2","0","3","0","-30","0","12","0","18","0","42","0","-12","0","-57","0","-2","0","-16","0","17","0","13","0","-8","0","11","0","6","0","-8","0","8","0","-40","0","-25","0","8","0","-60","0","-45","0"],"lmfdb":"agrees","curve":{"cremona":"308a1","lmfdb":"308.a","ainvs":[0,-1,0,-21,49],"rank":1,"torsion":1},"derived":{"al":[[2,null],[7,1],[11,-1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"308.2.a.b","letter":"b","dim":2,"charpoly":["3384","-120","1"],"traces":["2","0","0","0","4","0","-2","0","6","0","-2","0","4","0","0","0","4","0","0","0","0","0","8","0","-2","0","0","0","-4","0","8","0","0","0","-4","0","8","0","-12","0","-4","0","-4","0","12","0","-8","0","2","0","-12","0","0","0","-4","0","-24","0","0","0","-4","0","-6","0","8","0","0","0","-24","0","-16","0","20","0","0","0","2","0","-12","0","-18","0","-24","0","8","0","24","0","12","0","-4","0","12","0","0","0","20","0","-6","0","-12","0","24","0","0","0","-8","0","20","0","0","0","-20","0","16","0","12","0","-4","0","2","0","-36","0","-24","0","16","0","24","0","0","0","0","0","0","0","0","0","16","0","-12","0","-4","0","-8","0","0","0","4","0","-12","0","12","0","16","0","20","0","48","0","-8","0","8","0","0","0","8","0","-6","0","0","0","-4","0","2","0","36","0","8","0","28","0","36","0","16","0","-4","0","0","0","16","0","4","0","-24","0","-12","0","8","0","-72","0","4","0","-8","0","24","0","0","0","-40","0","-24","0","-8","0","-8","0","12","0","20","0","8","0","-6","0","-16","0","-20","0","0","0","-12","0","-16","0","-24","0","32","0","12","0","0","0","4","0","24","0","-24","0","0","0","-8","0","-24","0","12","0","-8","0","-12","0","0","0","0","0","0","0","-36","0","32","0","12","0","2","0","12","0","24","0","-20","0","-48","0","-48","0","4","0","-14","0","-24","0","-36","0","0","0","0","0","40","0","4","0","-12","0","-8","0","16","0","12","0","-8","0","-28","0","-12","0","12","0","4","0","0","0","24","0","-4","0","24","0","8","0","-64","0","24","0","0","0","12","0","0","0","-8","0","-2","0","-48","0","4","0","28","0","0","0","12","0","-32","0","12","0","-20","0","10","0","0","0","40","0","8","0","-12","0","0","0","28","0","0","0","-32","0","-16","0","-48","0","40","0","4","0","-12","0","12","0","40","0","48","0","-24","0","-12","0","24","0","-36","0","4","0","-36","0","-8","0","-28","0","48","0","0","0","-48","0","72","0","32","0","8","0","-24","0","-4","0","4","0","12","0","-28","0","52","0","48","0","48","0","-40","0","6","0","48","0","24","0","48","0","0","0","4","0","72","0","-8","0","-20","0","0","0","-60","0","-40","0","24","0","0","0","0","0","0","0","4","0","0","0","0","0","-8","0","16","0","24","0","40","0","64","0","24","0","36","0","-32","0","-12","0","16","0","-56","0","48","0","0","0","-24","0","-48","0","-20","0","-20","0","0","0","48","0","8","0","60","0","-28","0","-8","0","0","0","4","0","34","0","0","0","28","0","-16","0","-96","0","-2","0","4","0","-24","0","40","0","-24","0","-12","0","-48","0","12","0","0","0","-68","0","-32","0","12","0","16","0","-40","0","18","0","12","0","-40","0","-48","0","-8","0","4","0","96","0","24","0","0","0","24","0","48","0","-24","0","-96","0","-36","0","-8","0","108","0","-24","0","28","0","0","0","4","0","-8","0","-24","0","-4","0","-4","0","-72","0","0","0","16","0","0","0","-12","0","-38","0","24","0","16","0","-24","0","0","0","32","0","4","0","-48","0","24","0","-16","0","48","0","-24","0","0","0","-12","0","-28","0","0","0","60","0","20","0","-20","0","-48","0","0","0","-64","0","-84","0","4","0","44","0","0","0","4","0","-20","0","48","0","-72","0","0","0","24","0","-48","0","-48","0","6","0","32","0","28","0","24","0","-12","0","0","0","-24","0","12","0","-12","0","-36","0","8","0","-8","0","0","0","56","0","-24","0","-36","0","4","0","-8","0","-54","0","-32","0","76","0","0","0","0","0","-24","0","-48","0","0","0","8","0","-72","0","8","0","-16","0","12","0","-24","0","-44","0","24","0","36","0","-20","0","24","0","-36","0","44","0","-48","0","36","0","-8","0","0","0","72","0","16","0","0","0","40","0","-8","0","96","0","20","0","-44","0","96","0","-44","0","-4","0","36","0","-20","0","-16","0","24","0","-12","0","-8","0","-72","0","16","0","-48","0","-12","0","-12","0","-8","0","0","0","76","0","-28","0","48","0","4","0","16","0","0","0","24","0","-2","0","24","0","-12","0","-2","0","0","0","32","0","52","0","0","0","52","0","-16","0","36","0","-64","0","-8","0","-48","0","12","0","72","0","60","0","24","0","44","0","36","0","-12","0","-40","0","72","0","8","0","-16","0","18","0","24","0","16","0","-96","0","8","0","-48","0","-24","0","56","0","16","0","-36","0","24","0","24","0","72","0","0","0","48","0","-48","0","-8","0","-8","0","72","0","-36","0","0","0","12","0","-8","0","12","0","96","0","92","0","56","0","0","0","40","0","28","0","-96","0","-68","0","32","0","-24","0","0","0","-18","0","-24","0","8","0","-68","0","-48","0","-32","0","-16","0","12","0","28","0","-12","0","60","0","24","0","-24","0","12","0","-64","0","32","0","0","0","16","0","12","0","0","0"],"lmfdb":"agrees","derived":{"al":[[2,null],[7,1],[11,1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"308.2.a.c","letter":"c","dim":3,"charpoly":["12336","-2776","41","1"],"traces":["3","0","-1","0","-1","0","3","0","4","0","3","0","12","0","9","0","2","0","-2","0","-1","0","-7","0","18","0","-7","0","6","0","-9","0","-1","0","-1","0","7","0","0","0","-2","0","-4","0","-34","0","-4","0","3","0","-30","0","2","0","-1","0","26","0","-23","0","14","0","4","0","-28","0","-5","0","19","0","-5","0","-14","0","-48","0","3","0","14","0","-1","0","4","0","6","0","-10","0","-19","0","12","0","-35","0","18","0","15","0","4","0","-12","0","8","0","9","0","2","0","0","0","-11","0","17","0","-13","0","40","0","2","0","3","0","30","0","-3","0","38","0","-24","0","-34","0","-2","0","35","0","5","0","2","0","-20","0","12","0","46","0","-1","0","6","0","14","0","-4","0","-23","0","23","0","-18","0","-7","0","-4","0","9","0","50","0","37","0","-20","0","16","0","18","0","-5","0","39","0","-11","0","-18","0","-35","0","2","0","-7","0","-17","0","2","0","52","0","-18","0","4","0","-15","0","6","0","-6","0","6","0","-2","0","26","0","1","0","-16","0","-9","0","34","0","-28","0","-17","0","26","0","-4","0","17","0","-1","0","-30","0","-40","0","38","0","28","0","-12","0","-12","0","-1","0","0","0","-60","0","-63","0","-7","0","58","0","38","0","7","0","-40","0","38","0","-66","0","-53","0","-14","0","-8","0","0","0","18","0","-12","0","14","0","-32","0","0","0","-74","0","-2","0","45","0","-39","0","26","0","-1","0","-7","0","4","0","-4","0","8","0","-94","0","-52","0","-32","0","20","0","5","0","-34","0","-23","0","6","0","-18","0","-60","0","32","0","76","0","-4","0","25","0","42","0","17","0","50","0","71","0","-9","0","3","0","-39","0","14","0","-34","0","-52","0","29","0","-79","0","-30","0","12","0","-5","0","-1","0","-2","0","27","0","4","0","2","0","56","0","95","0","-32","0","-11","0","-46","0","-9","0","-1","0","12","0","25","0","-70","0","-6","0","78","0","22","0","26","0","38","0","-48","0","31","0","7","0","-18","0","23","0","-23","0","12","0","-10","0","60","0","-10","0","36","0","136","0","14","0","0","0","-32","0","-13","0","-14","0","38","0","-58","0","4","0","31","0","-61","0","14","0","-25","0","-2","0","38","0","-28","0","20","0","2","0","66","0","7","0","75","0","25","0","-5","0","1","0","-4","0","-96","0","68","0","76","0","52","0","19","0","-55","0","-15","0","44","0","26","0","76","0","-34","0","-5","0","-12","0","-50","0","8","0","-20","0","37","0","-79","0","-14","0","22","0","4","0","-4","0","-44","0","3","0","-40","0","-48","0","82","0","-4","0","-22","0","28","0","-66","0","29","0","3","0","-28","0","-29","0","52","0","0","0","108","0","-20","0","14","0","71","0","2","0","-24","0","-30","0","-44","0","127","0","-1","0","-62","0","12","0","-3","0","-124","0","11","0","34","0","4","0","2","0","-120","0","-16","0","-70","0","6","0","-42","0","6","0","4","0","40","0","-56","0","-22","0","-1","0","58","0","-10","0","4","0","-28","0","-58","0","10","0","-37","0","1","0","-19","0","109","0","26","0","-2","0","-31","0","-26","0","18","0","12","0","74","0","55","0","-55","0","56","0","-19","0","-23","0","-35","0","-33","0","-54","0","-12","0","30","0","-21","0","-176","0","18","0","-78","0","85","0","14","0","24","0","-44","0","30","0","15","0","36","0","12","0","-65","0","-57","0","56","0","-67","0","4","0","-114","0","-96","0","2","0","-20","0","-22","0","72","0","-12","0","-49","0","-64","0","-29","0","-28","0","-76","0","-53","0","8","0","16","0","116","0","35","0","-65","0","56","0","84","0","9","0","-5","0","-54","0","152","0","8","0","-98","0","-8","0","2","0","19","0","67","0","78","0","42","0","19","0","-56","0","0","0","-140","0","-96","0","-64","0","38","0","6","0","72","0","-11","0","60","0","-5","0","34","0","25","0","-74","0","-30","0","17","0","132","0","106","0","95","0","20","0","42","0","-14","0","-13","0","-54","0","18","0","-2","0","-56","0","84","0","-48","0","40","0","-18","0","53","0","-48","0","16","0","27","0","-64","0","2","0","14","0","-5","0","-53","0","37","0","20","0","-139","0","3","0","-16","0","-1","0","6","0","124","0","-36","0","13","0","30","0","-44","0","-112","0","69","0","14","0","-52","0","70","0","-3","0","-58","0","114","0","-17","0","-28","0","-35","0","154","0","38","0","-1","0","-40","0","-11","0","100","0","6","0","-12","0","-24","0","115","0","-32","0","8","0","-56","0","4","0","158","0","-34","0","48","0","52","0","60","0","44","0","4","0","54","0","-2","0","100","0","6","0","-4","0","75","0","-22","0","70","0","35","0","-53","0","-20","0","-17","0","40","0","-27","0","-10","0","5","0","48","0","68","0","130","0","46","0","4","0","-89","0","2","0","-252","0","53","0","-19","0","-52","0","-125","0","6","0","-20","0","-24","0","112","0","-85","0","136","0","-44","0","-49","0"],"lmfdb":"agrees","derived":{"al":[[2,null],[7,-1],[11,-1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.269,"computed":"atlas","estimate":{"seconds":0.323,"low":0.197,"high":0.558,"bytes":1945269},"url":"https://sagebrush.space/atlas/mf/308.2.a"}