{"label":"296.2.a","level":296,"weight":2,"dims":{"new":9,"cusp":35,"eisenstein":7,"modsym":77},"old":[[37,2,4],[74,4,3],[148,3,2]],"T":[[3,1],[5,1]],"status":"proven","checks":["dim M^+ at levels [1, 2, 4, 8, 37, 74, 148, 296]: [0, 1, 2, 3, 3, 11, 22, 42] (certified at ell = 2147483629)","T = [(3, 1), (5, 1)]; h of degree 9 = 1 x 9 (phi(ord eps) x dim S_k^new); 1 primes, 0 rejected"],"newforms":[{"label":"296.2.a.a","letter":"a","dim":1,"charpoly":["3","1"],"traces":["1","0","-1","0","-2","0","1","0","-2","0","1","0","-6","0","2","0","-4","0","-8","0","-1","0","6","0","-1","0","5","0","2","0","-4","0","-1","0","-2","0","-1","0","6","0","7","0","2","0","4","0","9","0","-6","0","4","0","-3","0","-2","0","8","0","-12","0","4","0","-2","0","12","0","0","0","-6","0","7","0","7","0","1","0","1","0","0","0","1","0","3","0","8","0","-2","0","-12","0","-6","0","4","0","16","0","-8","0","-2","0","-17","0","2","0","2","0","-4","0","16","0","1","0","2","0","-12","0","12","0","-4","0","-10","0","-7","0","12","0","-17","0","-2","0","0","0","-8","0","-10","0","-14","0","-4","0","-9","0","-6","0","-4","0","6","0","-9","0","0","0","8","0","8","0","19","0","3","0","6","0","-22","0","2","0","12","0","23","0","16","0","-3","0","-1","0","12","0","-22","0","-23","0","-4","0","2","0","-4","0","5","0","0","0","-10","0","-12","0","7","0","-14","0","0","0","2","0","-14","0","-12","0","-8","0","9","0","-7","0","-4","0","-4","0","-7","0","24","0","25","0","2","0","24","0","-5","0","-1","0","-2","0","-18","0","0","0","10","0","-30","0","-16","0","12","0","48","0","-3","0","26","0","6","0","-8","0","12","0","-1","0","-4","0","13","0","6","0","12","0","-6","0","-9","0","6","0","-1","0","12","0","8","0","-20","0","8","0","-16","0","7","0","-1","0","8","0","6","0","24","0","5","0","-36","0","2","0","17","0","-8","0","29","0","-2","0","24","0","18","0","4","0","-10","0","2","0","4","0","32","0","6","0","-16","0","9","0","-22","0","2","0","0","0","-9","0","-2","0","-4","0","-13","0","12","0","22","0","-26","0","-30","0","-36","0","-14","0","4","0","-25","0","45","0","10","0","-14","0","-16","0","-14","0","-3","0","1","0","-12","0","-12","0","37","0","17","0","-36","0","-2","0","-4","0","-12","0","-24","0","0","0","0","0","-1","0","8","0","-10","0","24","0","-2","0","-1","0","0","0","14","0","-12","0","-6","0","4","0","5","0","8","0","-18","0","4","0","4","0","6","0","10","0","-39","0","4","0","-48","0","-32","0","12","0","-13","0","24","0","9","0","20","0","7","0","0","0","12","0","18","0","-20","0","-6","0","-22","0","-8","0","18","0","0","0","-19","0","2","0","8","0","6","0","-18","0","6","0","-6","0","16","0","-20","0","22","0","-12","0","-8","0","4","0","7","0","4","0","-12","0","-8","0","34","0","-23","0","45","0","7","0","-40","0","-4","0","9","0","3","0","-17","0","6","0","1","0","16","0","13","0","24","0","-42","0","8","0","22","0","-6","0","-36","0","23","0","-32","0","-8","0","-8","0","-16","0","0","0","-2","0","14","0","-12","0","4","0","-22","0","-4","0","1","0","28","0","21","0","0","0","-6","0","32","0","10","0","3","0","-3","0","-24","0","-24","0","32","0","-7","0","3","0","8","0","14","0","15","0","10","0","0","0","20","0","32","0","-2","0","-54","0","35","0","14","0","9","0","5","0","30","0","-12","0","-19","0","8","0","4","0","20","0","-9","0","34","0","36","0","-14","0","31","0","14","0","4","0","-36","0","-12","0","4","0","-8","0","0","0","-14","0","-21","0","-36","0","-24","0","16","0","12","0","-25","0","4","0","11","0","-5","0","-15","0","-8","0","-24","0","42","0","28","0","5","0","18","0","52","0","-2","0","8","0","-28","0","2","0","24","0","8","0","18","0","-17","0","12","0","0","0","-24","0","12","0","-10","0","1","0","2","0","30","0","-2","0","-44","0","13","0","-8","0","19","0","-12","0","0","0","21","0","-48","0","43","0","18","0","-6","0","-4","0","-33","0","-26","0","0","0","10","0","-6","0","-27","0","16","0","-16","0","72","0","-10","0","-12","0","19","0","4","0","1","0","-56","0","7","0","10","0","-38","0","-39","0","-13","0","2","0","-24","0","-6","0","48","0","-36","0","24","0","7","0","-12","0","6","0","26","0","45","0","9","0","44","0","-16","0","12","0","29","0","-24","0","1","0","-54","0","-40","0","-12","0","24","0","-24","0","-20","0","36","0","-25","0","20","0","-46","0","-10","0","-8","0","-6","0","26","0","-32","0","-52","0","-32","0","-7","0","0","0","6","0","1","0","0","0","0","0","16","0","12","0","-22","0","-6","0","-30","0","20","0","-24","0","47","0","-17","0","1","0","-72","0","44","0","36","0","-8","0","12","0","-2","0","46","0","-32","0","34","0","-54","0","3","0","8","0","0","0","-14","0","-29","0","-42","0","1","0","-4","0","18","0","48","0","-24","0","8","0","-19","0","-18","0","14","0","42","0","-10","0","-52","0","-42","0","10","0","-19","0","0","0","-2","0","-14","0","-15","0","8","0","20","0","34","0","-32","0","-32","0","-4","0","-6","0","4","0","-12","0","-32","0","-9","0","-14","0","-9","0","12","0","-22","0","22","0","28","0","-6","0","-5","0"],"lmfdb":"agrees","curve":{"cremona":"296a1","lmfdb":"296.a","ainvs":[0,-1,0,-9,13],"rank":1,"torsion":1},"derived":{"al":[[2,null],[37,1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"296.2.a.b","letter":"b","dim":1,"charpoly":["1","1"],"traces":["1","0","-1","0","0","0","-3","0","-2","0","-3","0","0","0","0","0","2","0","-2","0","3","0","-6","0","-5","0","5","0","-2","0","-4","0","3","0","0","0","1","0","0","0","7","0","4","0","0","0","1","0","2","0","-2","0","9","0","0","0","2","0","8","0","-4","0","6","0","0","0","12","0","6","0","-5","0","-13","0","5","0","9","0","-10","0","1","0","-1","0","0","0","2","0","-2","0","0","0","4","0","0","0","-12","0","6","0","-9","0","-8","0","0","0","12","0","-14","0","-1","0","6","0","0","0","0","0","-6","0","-2","0","-7","0","0","0","11","0","-4","0","10","0","6","0","0","0","10","0","-20","0","-1","0","0","0","0","0","-2","0","-21","0","0","0","-4","0","0","0","-17","0","-9","0","18","0","8","0","0","0","-2","0","-13","0","4","0","-19","0","15","0","-8","0","10","0","5","0","4","0","0","0","-6","0","-15","0","-20","0","4","0","0","0","11","0","-14","0","-12","0","6","0","0","0","12","0","6","0","13","0","5","0","0","0","12","0","13","0","0","0","5","0","10","0","0","0","-13","0","-9","0","-18","0","0","0","10","0","-6","0","18","0","-16","0","0","0","0","0","1","0","-24","0","18","0","0","0","28","0","-3","0","4","0","-19","0","0","0","2","0","14","0","15","0","0","0","15","0","24","0","8","0","32","0","-8","0","0","0","-21","0","-13","0","12","0","22","0","0","0","-15","0","0","0","-12","0","9","0","0","0","-7","0","8","0","30","0","0","0","0","0","6","0","6","0","-12","0","-4","0","0","0","14","0","-3","0","-22","0","-2","0","0","0","15","0","-6","0","12","0","15","0","0","0","-10","0","22","0","0","0","-30","0","0","0","6","0","15","0","-15","0","2","0","0","0","-32","0","-14","0","-27","0","1","0","0","0","0","0","5","0","-11","0","-20","0","0","0","-8","0","20","0","-12","0","-10","0","0","0","-25","0","-6","0","28","0","0","0","0","0","-3","0","-32","0","-10","0","-24","0","0","0","20","0","-3","0","-10","0","-2","0","-10","0","12","0","0","0","0","0","21","0","0","0","12","0","32","0","-4","0","-41","0","0","0","21","0","-30","0","-21","0","0","0","0","0","28","0","10","0","-8","0","38","0","0","0","6","0","-36","0","17","0","-12","0","10","0","-18","0","-38","0","0","0","-18","0","0","0","26","0","-8","0","12","0","-4","0","0","0","15","0","0","0","2","0","-18","0","0","0","13","0","-15","0","39","0","-10","0","0","0","-3","0","19","0","-29","0","0","0","-15","0","-8","0","13","0","-16","0","0","0","0","0","-10","0","-6","0","-36","0","-5","0","0","0","12","0","8","0","4","0","30","0","0","0","18","0","0","0","6","0","0","0","0","0","-3","0","-24","0","-15","0","20","0","30","0","38","0","-4","0","3","0","-27","0","0","0","42","0","8","0","-11","0","11","0","0","0","14","0","23","0","14","0","-24","0","0","0","34","0","-6","0","0","0","43","0","0","0","-23","0","37","0","-30","0","6","0","25","0","-6","0","2","0","2","0","-13","0","0","0","0","0","10","0","-33","0","-34","0","0","0","-46","0","-24","0","-12","0","4","0","0","0","26","0","35","0","42","0","0","0","0","0","12","0","-5","0","12","0","-41","0","-25","0","-31","0","36","0","0","0","12","0","0","0","13","0","0","0","-28","0","-18","0","0","0","14","0","18","0","28","0","-2","0","0","0","27","0","6","0","20","0","24","0","0","0","6","0","13","0","24","0","-18","0","10","0","-26","0","13","0","8","0","31","0","0","0","-36","0","-3","0","0","0","31","0","0","0","2","0","-36","0","3","0","24","0","0","0","-26","0","-18","0","17","0","42","0","0","0","0","0","14","0","-28","0","-33","0","20","0","3","0","-14","0","15","0","-10","0","0","0","-39","0","19","0","-18","0","0","0","0","0","16","0","2","0","4","0","39","0","0","0","-14","0","-10","0","-27","0","-15","0","0","0","-8","0","0","0","-15","0","-48","0","-15","0","-38","0","-56","0","-24","0","4","0","0","0","-20","0","8","0","-25","0","-32","0","0","0","6","0","8","0","-6","0","34","0","0","0","6","0","-34","0","21","0","-48","0","0","0","13","0","30","0","0","0","24","0","0","0","-22","0","-22","0","18","0","32","0","0","0","-9","0","-33","0","-3","0","-2","0","0","0","0","0","8","0","18","0","12","0","0","0","-28","0","18","0","-4","0","3","0","0","0","-30","0","-4","0","7","0","0","0","-5","0","16","0","-10","0","-4","0","-30","0","0","0","17","0","0","0","-2","0","-42","0","0","0","-2","0","0","0","-6","0","45","0","0","0","-6","0","-30","0","-15","0","-24","0","0","0","-22","0","4","0","28","0","60","0","0","0","4","0","6","0","28","0","-33","0","0","0","3","0","-24","0","44","0","22","0","0","0","18","0","5","0"],"lmfdb":"agrees","curve":{"cremona":"296b1","lmfdb":"296.b","ainvs":[0,-1,0,-33,85],"rank":1,"torsion":1},"derived":{"al":[[2,null],[37,-1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"296.2.a.c","letter":"c","dim":3,"charpoly":["37","-21","-1","1"],"traces":["3","0","2","0","-1","0","7","0","3","0","0","0","3","0","10","0","-4","0","8","0","-3","0","9","0","-4","0","-1","0","-9","0","17","0","-9","0","-10","0","-3","0","-7","0","-16","0","-4","0","2","0","11","0","8","0","-18","0","-3","0","-9","0","-10","0","-2","0","15","0","12","0","-10","0","-5","0","3","0","-5","0","-6","0","-21","0","-15","0","-1","0","-25","0","-9","0","-14","0","-3","0","16","0","-8","0","22","0","-18","0","0","0","-24","0","-9","0","15","0","36","0","-7","0","44","0","-2","0","-10","0","-6","0","-21","0","16","0","39","0","-6","0","-12","0","7","0","46","0","-6","0","44","0","-15","0","1","0","-13","0","27","0","72","0","6","0","-39","0","-7","0","14","0","6","0","5","0","3","0","-19","0","16","0","26","0","-15","0","13","0","36","0","18","0","-19","0","11","0","-50","0","16","0","13","0","-16","0","1","0","-30","0","23","0","1","0","-10","0","-5","0","-33","0","2","0","32","0","-16","0","10","0","1","0","-30","0","50","0","-5","0","50","0","32","0","-13","0","-34","0","7","0","-2","0","-14","0","-43","0","-51","0","-11","0","16","0","-19","0","-5","0","6","0","-6","0","-47","0","-22","0","-23","0","-22","0","24","0","12","0","0","0","-7","0","-1","0","-1","0","-16","0","-32","0","26","0","-25","0","-54","0","-6","0","-27","0","20","0","12","0","34","0","52","0","-55","0","5","0","70","0","-68","0","-48","0","-30","0","33","0","-30","0","11","0","-31","0","-34","0","48","0","67","0","-36","0","2","0","30","0","-24","0","-75","0","40","0","-10","0","2","0","33","0","-14","0","-3","0","37","0","-54","0","48","0","-9","0","23","0","25","0","-84","0","48","0","-31","0","26","0","0","0","-32","0","47","0","15","0","122","0","-7","0","-14","0","-29","0","41","0","-5","0","-43","0","-33","0","-74","0","-33","0","-4","0","-36","0","24","0","61","0","-22","0","-22","0","-18","0","1","0","-44","0","24","0","8","0","16","0","0","0","50","0","36","0","16","0","-14","0","43","0","16","0","-1","0","38","0","46","0","68","0","135","0","-10","0","-16","0","-25","0","14","0","27","0","17","0","20","0","-48","0","3","0","4","0","39","0","12","0","-46","0","52","0","52","0","-18","0","-39","0","49","0","14","0","-80","0","19","0","-84","0","30","0","28","0","23","0","-3","0","-26","0","70","0","-40","0","60","0","-17","0","22","0","-33","0","11","0","6","0","-78","0","31","0","20","0","102","0","7","0","-29","0","48","0","33","0","-81","0","1","0","71","0","-52","0","-49","0","-38","0","-34","0","-30","0","23","0","-68","0","102","0","-27","0","15","0","19","0","-42","0","-54","0","22","0","-14","0","18","0","-10","0","-15","0","-88","0","-48","0","6","0","58","0","-71","0","52","0","88","0","30","0","-14","0","22","0","-10","0","27","0","-93","0","-31","0","36","0","30","0","-5","0","-62","0","-48","0","-26","0","-17","0","-67","0","-38","0","83","0","53","0","26","0","-70","0","-15","0","-71","0","-74","0","28","0","-13","0","68","0","-11","0","-84","0","4","0","-77","0","15","0","-40","0","-19","0","16","0","16","0","-8","0","-34","0","25","0","84","0","18","0","-35","0","-16","0","-30","0","8","0","-9","0","-66","0","-88","0","-35","0","43","0","-21","0","-64","0","42","0","-9","0","-36","0","12","0","14","0","35","0","-91","0","-96","0","20","0","-48","0","56","0","-14","0","41","0","41","0","-8","0","44","0","-69","0","-49","0","1","0","48","0","63","0","-8","0","21","0","22","0","50","0","14","0","43","0","18","0","-36","0","-85","0","80","0","99","0","-16","0","-94","0","61","0","10","0","22","0","70","0","11","0","-42","0","-2","0","11","0","21","0","-24","0","108","0","-8","0","82","0","-30","0","82","0","59","0","-41","0","3","0","-78","0","-63","0","13","0","16","0","5","0","43","0","-34","0","-6","0","38","0","-117","0","0","0","4","0","72","0","-42","0","106","0","-8","0","60","0","9","0","34","0","-52","0","-36","0","-3","0","-48","0","0","0","-32","0","-1","0","-4","0","96","0","-91","0","-21","0","82","0","-52","0","-16","0","66","0","22","0","20","0","-9","0","-53","0","0","0","-8","0","-48","0","17","0","-20","0","20","0","10","0","-6","0","94","0","34","0","-10","0","30","0","-94","0","31","0","16","0","14","0","59","0","-21","0","15","0","44","0","86","0","24","0","-48","0","100","0","178","0","6","0","36","0","-40","0","-14","0","-93","0","83","0","-44","0","2","0","-76","0","-68","0","4","0","40","0","35","0","128","0","69","0","-18","0","70","0","-76","0","16","0","-35","0","-58","0","28","0","66","0","-14","0","12","0","29","0","-21","0","-66","0","14","0","9","0","0","0","-41","0","-28","0","25","0","-46","0","-21","0","-52","0","36","0","22","0","55","0","28","0","75","0","-40","0","17","0","-6","0","-28","0","6","0","1","0"],"lmfdb":"agrees","derived":{"al":[[2,null],[37,1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"296.2.a.d","letter":"d","dim":4,"charpoly":["-2","39","1","-7","1"],"traces":["4","0","2","0","5","0","-1","0","8","0","4","0","5","0","0","0","8","0","2","0","1","0","-9","0","7","0","-1","0","7","0","-1","0","3","0","-12","0","4","0","-15","0","2","0","6","0","0","0","-29","0","9","0","4","0","-5","0","-5","0","-32","0","-10","0","-1","0","-28","0","-2","0","-1","0","-27","0","-17","0","8","0","19","0","-27","0","15","0","-8","0","15","0","10","0","-17","0","-20","0","34","0","-6","0","-34","0","2","0","44","0","9","0","27","0","-46","0","1","0","-4","0","2","0","16","0","22","0","-17","0","-2","0","-4","0","22","0","12","0","3","0","8","0","8","0","18","0","17","0","-29","0","51","0","-49","0","-22","0","22","0","41","0","11","0","14","0","16","0","41","0","21","0","37","0","16","0","20","0","17","0","-67","0","7","0","22","0","35","0","15","0","26","0","-4","0","3","0","-8","0","5","0","8","0","-9","0","11","0","6","0","-61","0","5","0","62","0","-36","0","-40","0","-20","0","-65","0","20","0","-26","0","71","0","-34","0","-84","0","15","0","10","0","7","0","-31","0","6","0","19","0","-7","0","39","0","-62","0","-91","0","-15","0","20","0","-26","0","17","0","54","0","-35","0","4","0","-56","0","0","0","14","0","-1","0","39","0","-21","0","-22","0","-46","0","-8","0","-25","0","88","0","-38","0","5","0","40","0","-22","0","-6","0","-88","0","-51","0","-52","0","-78","0","30","0","44","0","-10","0","25","0","20","0","51","0","61","0","-30","0","14","0","-21","0","-12","0","-98","0","40","0","32","0","21","0","4","0","10","0","-68","0","-11","0","-26","0","8","0","-17","0","12","0","84","0","41","0","-29","0","-3","0","-40","0","-30","0","-27","0","46","0","-62","0","2","0","-25","0","64","0","-26","0","-83","0","10","0","77","0","41","0","9","0","27","0","-9","0","14","0","71","0","-40","0","-86","0","32","0","25","0","-18","0","-24","0","62","0","-65","0","158","0","-28","0","-80","0","44","0","4","0","68","0","20","0","36","0","56","0","-5","0","-8","0","45","0","-14","0","14","0","-32","0","-57","0","24","0","-18","0","31","0","-26","0","29","0","46","0","96","0","-40","0","-33","0","20","0","75","0","88","0","74","0","-64","0","-2","0","34","0","-57","0","121","0","70","0","8","0","119","0","26","0","-84","0","-34","0","17","0","5","0","-10","0","34","0","18","0","-30","0","-97","0","14","0","89","0","-5","0","-10","0","-36","0","-73","0","-66","0","34","0","1","0","15","0","-70","0","33","0","15","0","133","0","-11","0","-2","0","-69","0","-2","0","31","0","-110","0","-69","0","-12","0","-10","0","37","0","-73","0","87","0","-78","0","-22","0","-32","0","18","0","4","0","0","0","-11","0","24","0","6","0","0","0","10","0","5","0","42","0","-116","0","62","0","42","0","-46","0","-24","0","-117","0","-29","0","-115","0","-30","0","-74","0","115","0","-12","0","-24","0","38","0","7","0","51","0","6","0","39","0","45","0","-22","0","-20","0","11","0","49","0","-80","0","52","0","13","0","-50","0","-34","0","-134","0","8","0","11","0","59","0","46","0","-59","0","16","0","-14","0","-72","0","-58","0","-51","0","-100","0","-158","0","5","0","-68","0","92","0","72","0","-35","0","-30","0","24","0","-7","0","-45","0","-31","0","-18","0","42","0","81","0","-80","0","-88","0","44","0","-19","0","-71","0","-6","0","56","0","-60","0","160","0","4","0","-35","0","57","0","2","0","-42","0","7","0","-15","0","-21","0","8","0","-113","0","76","0","9","0","56","0","-10","0","-20","0","-41","0","-121","0","12","0","-59","0","76","0","7","0","24","0","66","0","-19","0","28","0","106","0","38","0","39","0","84","0","-34","0","11","0","-41","0","38","0","38","0","0","0","-10","0","-12","0","-62","0","33","0","-7","0","1","0","4","0","33","0","-9","0","62","0","-55","0","91","0","2","0","-26","0","-16","0","-61","0","-58","0","30","0","84","0","166","0","-34","0","-86","0","28","0","13","0","50","0","76","0","52","0","-81","0","-40","0","80","0","0","0","15","0","0","0","18","0","-63","0","37","0","42","0","-45","0","-44","0","66","0","-22","0","148","0","-9","0","87","0","-52","0","92","0","14","0","-47","0","16","0","18","0","-26","0","-36","0","42","0","52","0","98","0","40","0","-106","0","17","0","-32","0","54","0","-53","0","-53","0","-65","0","106","0","58","0","28","0","88","0","-10","0","96","0","-80","0","-16","0","86","0","24","0","91","0","87","0","38","0","16","0","48","0","-110","0","7","0","-8","0","-31","0","-80","0","53","0","-10","0","12","0","-78","0","2","0","-121","0","-12","0","50","0","16","0","-102","0","6","0","169","0","-43","0","-126","0","87","0","-23","0","-72","0","-11","0","-64","0","77","0","-94","0","-21","0","-94","0","50","0","28","0","-17","0","2","0","95","0","-80","0","29","0","-22","0","16","0","84","0","-1","0"],"lmfdb":"agrees","derived":{"al":[[2,null],[37,-1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.277,"computed":"atlas","estimate":{"seconds":0.302,"low":0.184,"high":0.523,"bytes":1931958},"url":"https://sagebrush.space/atlas/mf/296.2.a"}