{"label":"176.2.a","level":176,"weight":2,"dims":{"new":5,"cusp":19,"eisenstein":11,"modsym":49},"old":[[11,1,5],[44,1,3],[88,3,2]],"T":[[3,1],[5,3]],"status":"proven","checks":["dim M^+ at levels [1, 2, 4, 8, 11, 16, 22, 44, 88, 176]: [0, 1, 2, 3, 2, 4, 5, 9, 16, 28] (certified at ell = 2147482921)","T = [(3, 1), (5, 3)]; h of degree 5 = 1 x 5 (phi(ord eps) x dim S_k^new); 1 primes, 0 rejected"],"newforms":[{"label":"176.2.a.a","letter":"a","dim":1,"charpoly":["10","1"],"traces":["1","0","-1","0","-3","0","-2","0","-2","0","1","0","-4","0","3","0","6","0","-8","0","2","0","3","0","4","0","5","0","0","0","-5","0","-1","0","6","0","-1","0","4","0","0","0","10","0","6","0","0","0","-3","0","-6","0","-6","0","-3","0","8","0","-3","0","-4","0","4","0","12","0","1","0","-3","0","-15","0","-4","0","-4","0","-2","0","-2","0","1","0","-6","0","-18","0","0","0","-9","0","8","0","5","0","24","0","-7","0","-2","0","18","0","-8","0","-6","0","-6","0","2","0","1","0","-15","0","-9","0","8","0","-12","0","1","0","0","0","3","0","16","0","-10","0","6","0","16","0","-15","0","9","0","-14","0","0","0","-4","0","0","0","3","0","6","0","10","0","-12","0","15","0","5","0","6","0","-6","0","4","0","3","0","12","0","3","0","16","0","18","0","-8","0","3","0","9","0","-13","0","4","0","3","0","6","0","-10","0","21","0","20","0","-12","0","6","0","-8","0","-1","0","0","0","0","0","-6","0","-8","0","-20","0","15","0","-30","0","10","0","4","0","-24","0","-17","0","-8","0","-6","0","-13","0","2","0","-24","0","0","0","2","0","-6","0","8","0","-16","0","9","0","32","0","6","0","9","0","3","0","18","0","-18","0","2","0","0","0","-18","0","18","0","9","0","-6","0","-20","0","-8","0","4","0","-10","0","10","0","-18","0","4","0","-24","0","0","0","19","0","7","0","0","0","9","0","5","0","-12","0","-20","0","-18","0","12","0","16","0","8","0","-12","0","-1","0","-12","0","33","0","0","0","6","0","-48","0","-16","0","-2","0","0","0","7","0","2","0","-3","0","2","0","15","0","-5","0","20","0","9","0","-12","0","14","0","-20","0","-21","0","45","0","12","0","36","0","45","0","-1","0","12","0","19","0","0","0","12","0","-10","0","-3","0","0","0","-29","0","-16","0","27","0","6","0","-20","0","-27","0","18","0","-6","0","6","0","-34","0","-16","0","18","0","20","0","-3","0","-1","0","2","0","-9","0","6","0","18","0","14","0","-12","0","-10","0","0","0","24","0","8","0","4","0","-18","0","29","0","0","0","-24","0","-8","0","6","0","21","0","27","0","-6","0","3","0","0","0","-10","0","-24","0","-28","0","30","0","12","0","-23","0","-15","0","-3","0","-2","0","-5","0","10","0","-32","0","12","0","12","0","4","0","6","0","21","0","-29","0","-4","0","-24","0","0","0","6","0","30","0","4","0","-12","0","30","0","-54","0","-3","0","-21","0","8","0","-40","0","24","0","0","0","-18","0","-27","0","-8","0","8","0","-30","0","-14","0","6","0","0","0","18","0","-9","0","-3","0","-16","0","13","0","-6","0","-8","0","8","0","0","0","4","0","-3","0","-18","0","-40","0","-6","0","36","0","45","0","-2","0","0","0","-44","0","-21","0","12","0","17","0","-20","0","12","0","-6","0","-24","0","12","0","40","0","-6","0","-36","0","36","0","8","0","0","0","26","0","-2","0","-3","0","-14","0","0","0","0","0","32","0","0","0","18","0","-17","0","15","0","18","0","-29","0","8","0","-6","0","43","0","20","0","-48","0","12","0","30","0","39","0","13","0","30","0","-3","0","-3","0","-10","0","3","0","-18","0","8","0","42","0","17","0","24","0","-48","0","0","0","17","0","-4","0","-34","0","20","0","-42","0","14","0","6","0","-48","0","-27","0","13","0","24","0","1","0","4","0","42","0","0","0","24","0","18","0","8","0","0","0","-36","0","-37","0","4","0","-15","0","12","0","6","0","-45","0","16","0","-8","0","0","0","-17","0","13","0","60","0","-4","0","-9","0","1","0","34","0","-32","0","-12","0","-18","0","12","0","12","0","-35","0","-9","0","-30","0","-22","0","-3","0","36","0","-4","0","36","0","12","0","44","0","18","0","42","0","-20","0","-2","0","0","0","-15","0","0","0","-15","0","-32","0","18","0","30","0","16","0","-18","0","9","0","0","0","18","0","-4","0","18","0","6","0","-24","0","-38","0","20","0","-12","0","-80","0","-16","0","30","0","43","0","-4","0","36","0","-19","0","10","0","-18","0","-36","0","-25","0","39","0","-29","0","18","0","-9","0","-2","0","-4","0","-3","0","38","0","-48","0","24","0","25","0","0","0","-48","0","-54","0","-19","0","-2","0","-4","0","14","0","-6","0","-52","0","0","0","-27","0","4","0","-9","0","-30","0","-32","0","1","0","0","0","-27","0","12","0","0","0","-36","0","20","0","39","0","4","0","-36","0","-12","0","-6","0","-12","0","-12","0","34","0","-16","0","60","0","-4","0","16","0","18","0","24","0","12","0","-18","0","32","0","1","0","-30","0","0","0","30","0","-27","0","16","0","-33","0","42","0","-63","0","0","0","-18","0","-6","0","12","0","-60","0","16","0","48","0","15","0","28","0","16","0","45","0","-9","0","-4","0","-45","0","-18","0","0","0","30","0","16","0","-7","0","24","0","-10","0","-5","0"],"lmfdb":"agrees","curve":{"cremona":"176c1","lmfdb":"176.a","ainvs":[0,-1,0,3,1],"rank":1,"torsion":1},"derived":{"al":[[2,null],[11,-1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"176.2.a.b","letter":"b","dim":1,"charpoly":["-4","1"],"traces":["1","0","1","0","1","0","2","0","-2","0","-1","0","4","0","1","0","-2","0","0","0","2","0","1","0","-4","0","-5","0","0","0","-7","0","-1","0","2","0","3","0","4","0","-8","0","6","0","-2","0","-8","0","-3","0","-2","0","-6","0","-1","0","0","0","-5","0","12","0","-4","0","4","0","7","0","1","0","3","0","4","0","-4","0","-2","0","10","0","1","0","6","0","-2","0","0","0","15","0","8","0","-7","0","0","0","-7","0","2","0","2","0","16","0","2","0","-18","0","10","0","3","0","9","0","1","0","-8","0","-4","0","1","0","-8","0","-9","0","-8","0","6","0","18","0","0","0","-5","0","-7","0","-10","0","-8","0","-4","0","0","0","-3","0","-10","0","-2","0","4","0","-7","0","-7","0","-6","0","2","0","-4","0","-1","0","12","0","3","0","0","0","-6","0","-8","0","-5","0","15","0","7","0","12","0","3","0","2","0","-10","0","-17","0","4","0","4","0","-2","0","0","0","7","0","0","0","-8","0","-2","0","0","0","-12","0","3","0","6","0","-14","0","4","0","-8","0","-19","0","8","0","-18","0","15","0","-2","0","24","0","-8","0","10","0","30","0","-8","0","16","0","-3","0","0","0","6","0","23","0","-1","0","-2","0","-2","0","6","0","0","0","-14","0","-6","0","15","0","10","0","28","0","8","0","4","0","-2","0","14","0","-18","0","-4","0","0","0","-16","0","-13","0","-7","0","24","0","-5","0","5","0","4","0","12","0","2","0","12","0","-8","0","16","0","-12","0","-1","0","-4","0","13","0","0","0","-18","0","0","0","-16","0","10","0","-16","0","-7","0","-6","0","7","0","-22","0","9","0","7","0","-20","0","1","0","-28","0","30","0","-20","0","-21","0","3","0","-4","0","20","0","-19","0","1","0","4","0","17","0","16","0","-12","0","-26","0","-9","0","0","0","5","0","-8","0","1","0","-2","0","-12","0","-15","0","-2","0","18","0","10","0","-2","0","0","0","2","0","-28","0","1","0","-3","0","-30","0","-7","0","-10","0","6","0","-10","0","-20","0","22","0","16","0","8","0","24","0","-4","0","18","0","-11","0","0","0","0","0","-40","0","6","0","11","0","15","0","-10","0","35","0","8","0","-2","0","8","0","-12","0","10","0","12","0","11","0","-7","0","27","0","14","0","-7","0","-6","0","0","0","12","0","-20","0","12","0","2","0","-7","0","-23","0","-4","0","8","0","0","0","2","0","6","0","-20","0","12","0","26","0","2","0","3","0","15","0","8","0","0","0","16","0","8","0","-6","0","-3","0","16","0","-8","0","14","0","-22","0","10","0","-32","0","-18","0","15","0","3","0","-8","0","7","0","10","0","-8","0","-24","0","0","0","20","0","3","0","-2","0","24","0","2","0","-4","0","9","0","2","0","0","0","28","0","-17","0","-4","0","33","0","4","0","12","0","6","0","-8","0","-28","0","0","0","-2","0","44","0","-4","0","0","0","-40","0","2","0","-14","0","1","0","22","0","0","0","-32","0","-16","0","-8","0","18","0","25","0","-5","0","30","0","11","0","0","0","-6","0","-7","0","-12","0","-8","0","-12","0","-6","0","-33","0","-29","0","6","0","7","0","5","0","-14","0","-41","0","18","0","-8","0","-10","0","37","0","-8","0","0","0","0","0","-19","0","-12","0","14","0","20","0","-42","0","-14","0","-18","0","16","0","-7","0","15","0","-24","0","-17","0","4","0","-10","0","16","0","24","0","2","0","0","0","-8","0","4","0","-25","0","-20","0","-7","0","-4","0","30","0","-15","0","32","0","-8","0","0","0","-3","0","13","0","-12","0","-36","0","-3","0","-7","0","-50","0","0","0","-4","0","-10","0","-12","0","-36","0","23","0","23","0","-2","0","-22","0","-1","0","12","0","20","0","4","0","-20","0","20","0","-2","0","-6","0","28","0","6","0","0","0","-3","0","0","0","-7","0","32","0","-14","0","18","0","48","0","-6","0","53","0","16","0","-30","0","-4","0","2","0","10","0","0","0","38","0","28","0","-4","0","0","0","-16","0","22","0","-39","0","4","0","52","0","25","0","-2","0","6","0","12","0","35","0","5","0","-29","0","-18","0","3","0","2","0","-4","0","3","0","14","0","0","0","8","0","15","0","-16","0","-24","0","-6","0","-13","0","-10","0","28","0","14","0","-18","0","-12","0","24","0","-43","0","-4","0","-5","0","22","0","-16","0","-1","0","0","0","15","0","4","0","0","0","12","0","12","0","7","0","12","0","-4","0","-12","0","-6","0","12","0","36","0","-10","0","-8","0","12","0","-12","0","-32","0","-30","0","0","0","-12","0","2","0","8","0","-1","0","42","0","-8","0","-10","0","27","0","16","0","13","0","34","0","-17","0","0","0","-14","0","18","0","36","0","4","0","32","0","0","0","-47","0","-20","0","-16","0","-27","0","-15","0","-20","0","-39","0","-2","0","-16","0","6","0","8","0","-7","0","0","0","38","0","-15","0"],"lmfdb":"agrees","curve":{"cremona":"176b1","lmfdb":"176.b","ainvs":[0,1,0,-5,-13],"rank":0,"torsion":1},"derived":{"al":[[2,null],[11,1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"176.2.a.c","letter":"c","dim":1,"charpoly":["6","1"],"traces":["1","0","3","0","-3","0","2","0","6","0","1","0","0","0","-9","0","-6","0","-4","0","6","0","-1","0","4","0","9","0","-8","0","7","0","3","0","-6","0","-1","0","0","0","4","0","-6","0","-18","0","8","0","-3","0","-18","0","2","0","-3","0","-12","0","1","0","4","0","12","0","0","0","5","0","-3","0","-3","0","16","0","12","0","2","0","-2","0","9","0","2","0","18","0","-24","0","15","0","0","0","21","0","12","0","-7","0","6","0","-10","0","16","0","-18","0","-2","0","-14","0","-3","0","-7","0","3","0","0","0","-12","0","1","0","12","0","3","0","-4","0","-18","0","2","0","-8","0","-27","0","-15","0","22","0","24","0","0","0","24","0","-9","0","18","0","18","0","-36","0","-21","0","-11","0","6","0","-2","0","4","0","-9","0","-16","0","-13","0","-24","0","18","0","8","0","3","0","5","0","-5","0","12","0","3","0","-6","0","18","0","9","0","4","0","0","0","6","0","-8","0","15","0","-16","0","-12","0","-6","0","-4","0","-20","0","-9","0","18","0","14","0","48","0","0","0","-29","0","24","0","-18","0","-21","0","6","0","-16","0","-24","0","-6","0","2","0","0","0","0","0","9","0","0","0","6","0","13","0","-1","0","54","0","-10","0","-2","0","-48","0","-14","0","-6","0","45","0","26","0","0","0","0","0","4","0","-2","0","42","0","6","0","-4","0","36","0","8","0","19","0","-21","0","12","0","-3","0","9","0","0","0","-12","0","-30","0","-12","0","4","0","48","0","12","0","-9","0","-36","0","-15","0","-8","0","-6","0","24","0","0","0","-42","0","16","0","35","0","-6","0","-15","0","-10","0","-21","0","7","0","-20","0","9","0","32","0","-14","0","0","0","3","0","9","0","-36","0","-24","0","-3","0","3","0","-48","0","-33","0","24","0","4","0","-22","0","9","0","0","0","-25","0","-12","0","-1","0","-6","0","-36","0","13","0","6","0","6","0","6","0","-26","0","-24","0","-6","0","0","0","-27","0","-1","0","34","0","-45","0","2","0","-6","0","66","0","28","0","30","0","48","0","-24","0","8","0","0","0","26","0","13","0","72","0","4","0","32","0","-18","0","9","0","-45","0","54","0","-21","0","4","0","54","0","0","0","12","0","-54","0","-28","0","-27","0","-63","0","33","0","10","0","-33","0","-6","0","-16","0","12","0","-8","0","0","0","-6","0","21","0","-9","0","12","0","-8","0","48","0","-18","0","-6","0","20","0","-48","0","30","0","30","0","-39","0","-13","0","32","0","-36","0","-48","0","8","0","54","0","37","0","-44","0","24","0","-42","0","-22","0","6","0","0","0","6","0","15","0","-3","0","12","0","-15","0","42","0","0","0","24","0","32","0","-4","0","9","0","42","0","0","0","-18","0","12","0","21","0","18","0","-24","0","4","0","27","0","-4","0","-23","0","12","0","4","0","2","0","0","0","-12","0","-28","0","18","0","-4","0","36","0","-24","0","-48","0","38","0","30","0","-3","0","18","0","-48","0","0","0","-16","0","-36","0","18","0","3","0","-9","0","30","0","-29","0","-12","0","6","0","-9","0","-60","0","12","0","0","0","-18","0","-9","0","-7","0","54","0","-15","0","1","0","42","0","11","0","-6","0","96","0","-22","0","-7","0","0","0","24","0","8","0","-87","0","4","0","-34","0","36","0","-30","0","-14","0","-54","0","-8","0","45","0","-63","0","0","0","29","0","12","0","-66","0","-24","0","-48","0","-10","0","4","0","-72","0","-20","0","19","0","-12","0","-7","0","0","0","6","0","23","0","32","0","0","0","-32","0","35","0","-27","0","36","0","4","0","27","0","5","0","26","0","0","0","36","0","-54","0","12","0","-4","0","-23","0","39","0","-54","0","10","0","-3","0","0","0","-28","0","108","0","0","0","16","0","-30","0","-6","0","28","0","-6","0","-16","0","-3","0","-72","0","33","0","-24","0","-42","0","-14","0","0","0","-18","0","1","0","-48","0","90","0","16","0","6","0","78","0","12","0","26","0","0","0","-12","0","24","0","0","0","-34","0","31","0","12","0","16","0","-35","0","-6","0","18","0","48","0","63","0","-21","0","35","0","18","0","39","0","2","0","-12","0","1","0","-26","0","72","0","-24","0","-11","0","24","0","16","0","-54","0","57","0","-2","0","0","0","-42","0","6","0","56","0","36","0","-19","0","28","0","-9","0","34","0","-8","0","9","0","-32","0","-15","0","0","0","-56","0","-12","0","-36","0","15","0","-28","0","-60","0","-36","0","2","0","-36","0","4","0","50","0","12","0","0","0","-4","0","96","0","-22","0","12","0","36","0","18","0","4","0","-27","0","10","0","-4","0","-54","0","-47","0","0","0","-45","0","-34","0","-27","0","-24","0","-30","0","18","0","-12","0","-12","0","8","0","72","0","-53","0","44","0","0","0","-11","0","15","0","-84","0","-25","0","-18","0","48","0","6","0","-16","0","105","0","24","0","2","0","-9","0"],"lmfdb":"agrees","curve":{"cremona":"176a1","lmfdb":"176.c","ainvs":[0,0,0,-4,-4],"rank":0,"torsion":1},"derived":{"al":[[2,null],[11,-1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"176.2.a.d","letter":"d","dim":2,"charpoly":["-52","-8","1"],"traces":["2","0","-1","0","3","0","2","0","3","0","2","0","-2","0","7","0","4","0","8","0","-18","0","-9","0","3","0","-7","0","-2","0","7","0","-1","0","-14","0","-11","0","-16","0","6","0","6","0","-4","0","-16","0","22","0","-2","0","8","0","3","0","-4","0","5","0","-6","0","20","0","-20","0","-15","0","13","0","5","0","2","0","24","0","2","0","14","0","-14","0","-10","0","6","0","-16","0","-7","0","32","0","5","0","12","0","27","0","3","0","-4","0","0","0","-10","0","2","0","8","0","-3","0","-5","0","-5","0","14","0","4","0","2","0","-20","0","15","0","4","0","14","0","-2","0","8","0","-19","0","-21","0","-22","0","8","0","-2","0","-20","0","-45","0","-8","0","-6","0","6","0","19","0","-13","0","30","0","-26","0","8","0","7","0","-16","0","10","0","12","0","8","0","-48","0","-45","0","17","0","-15","0","20","0","-25","0","4","0","10","0","25","0","-10","0","-24","0","4","0","-8","0","-1","0","32","0","-8","0","-22","0","8","0","16","0","23","0","26","0","-10","0","16","0","-4","0","3","0","-21","0","-38","0","17","0","-18","0","10","0","-24","0","10","0","18","0","50","0","28","0","-1","0","-8","0","22","0","1","0","-9","0","14","0","40","0","6","0","14","0","-30","0","46","0","29","0","8","0","24","0","-16","0","3","0","-36","0","2","0","16","0","-40","0","28","0","40","0","-26","0","-5","0","18","0","-35","0","-7","0","-8","0","-28","0","2","0","8","0","32","0","0","0","-36","0","1","0","-4","0","-49","0","-2","0","50","0","16","0","-54","0","30","0","-16","0","-41","0","-8","0","-31","0","16","0","11","0","7","0","76","0","-23","0","4","0","-48","0","24","0","-11","0","33","0","-36","0","24","0","-6","0","-1","0","20","0","-17","0","26","0","-60","0","0","0","1","0","36","0","-21","0","-36","0","-33","0","-14","0","-8","0","3","0","-18","0","-50","0","38","0","-12","0","-72","0","28","0","-24","0","-21","0","-11","0","12","0","19","0","90","0","2","0","-6","0","32","0","-28","0","-24","0","6","0","-40","0","-16","0","-46","0","-33","0","-24","0","-36","0","24","0","67","0","-35","0","15","0","38","0","-3","0","6","0","54","0","48","0","-10","0","-14","0","-6","0","-43","0","33","0","-3","0","2","0","15","0","6","0","12","0","-22","0","32","0","28","0","98","0","49","0","-1","0","-4","0","-44","0","-4","0","-4","0","-46","0","-8","0","8","0","22","0","-6","0","29","0","17","0","-32","0","-28","0","0","0","-16","0","30","0","15","0","24","0","24","0","14","0","3","0","50","0","28","0","54","0","-17","0","22","0","10","0","33","0","46","0","68","0","-26","0","-8","0","-20","0","-47","0","-24","0","-40","0","-2","0","-16","0","1","0","-14","0","-62","0","0","0","-21","0","12","0","27","0","-12","0","-44","0","8","0","4","0","16","0","28","0","-70","0","-18","0","-28","0","72","0","32","0","24","0","-14","0","3","0","34","0","-16","0","16","0","-34","0","4","0","28","0","-9","0","23","0","-58","0","16","0","-4","0","-22","0","47","0","-76","0","-28","0","46","0","-18","0","-39","0","-27","0","38","0","-23","0","5","0","-46","0","25","0","-54","0","-14","0","-18","0","63","0","-32","0","-56","0","-8","0","41","0","-6","0","-16","0","-36","0","8","0","10","0","2","0","36","0","-23","0","17","0","-76","0","57","0","20","0","-50","0","12","0","-56","0","68","0","-44","0","-56","0","-4","0","25","0","4","0","-23","0","-20","0","-26","0","-9","0","0","0","-8","0","-54","0","59","0","-6","0","12","0","-6","0","43","0","-15","0","30","0","-64","0","28","0","22","0","-32","0","-100","0","-7","0","-9","0","42","0","48","0","13","0","2","0","-60","0","-8","0","80","0","10","0","-54","0","32","0","36","0","82","0","24","0","5","0","24","0","-11","0","76","0","-2","0","-22","0","-28","0","62","0","-49","0","-32","0","-36","0","2","0","46","0","-106","0","-50","0","6","0","56","0","12","0","24","0","48","0","-20","0","39","0","24","0","-28","0","59","0","18","0","44","0","-24","0","-33","0","19","0","-22","0","26","0","49","0","2","0","20","0","41","0","-60","0","-16","0","-14","0","-23","0","-88","0","40","0","46","0","13","0","14","0","32","0","32","0","-2","0","86","0","-60","0","15","0","16","0","-25","0","-22","0","72","0","-14","0","-64","0","17","0","72","0","-24","0","16","0","-20","0","3","0","0","0","-6","0","4","0","-10","0","-4","0","100","0","-38","0","52","0","-56","0","-42","0","0","0","60","0","88","0","52","0","6","0","-10","0","-43","0","-48","0","-44","0","66","0","13","0","-36","0","67","0","-16","0","29","0","-16","0","-38","0","-29","0","-48","0","-32","0","-16","0","-8","0","-1","0","12","0","-24","0","87","0","-7","0","-22","0","-33","0","-62","0","144","0","-10","0","-24","0","-39","0","56","0","88","0","47","0"],"lmfdb":"agrees","derived":{"al":[[2,null],[11,-1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.209,"computed":"atlas","estimate":{"seconds":0.255,"low":0.155,"high":0.441,"bytes":1877582},"url":"https://sagebrush.space/atlas/mf/176.2.a"}