{"label":"324.2.a","level":324,"weight":2,"dims":{"new":4,"cusp":37,"eisenstein":35,"modsym":109},"old":[[27,1,6],[36,1,3],[54,2,4],[81,2,3],[108,1,2],[162,4,2]],"T":[[5,1],[7,3],[11,5],[13,7]],"status":"proven","checks":["dim M^+ at levels [1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324]: [0, 1, 1, 2, 3, 2, 5, 5, 4, 9, 11, 10, 21, 29, 57] (certified at ell = 2147483179)","T = [(5, 1), (7, 3), (11, 5), (13, 7)]; h of degree 4 = 1 x 4 (phi(ord eps) x dim S_k^new); 1 primes, 0 rejected"],"newforms":[{"label":"324.2.a.a","letter":"a","dim":1,"charpoly":["28","1"],"traces":["1","0","0","0","-3","0","-1","0","0","0","-3","0","-1","0","0","0","-6","0","-4","0","0","0","3","0","4","0","0","0","-3","0","5","0","0","0","3","0","2","0","0","0","-3","0","-1","0","0","0","9","0","-6","0","0","0","6","0","9","0","0","0","3","0","-13","0","0","0","3","0","-7","0","0","0","12","0","-10","0","0","0","3","0","11","0","0","0","9","0","18","0","0","0","-6","0","1","0","0","0","12","0","11","0","0","0","-15","0","-7","0","0","0","-12","0","2","0","0","0","9","0","-9","0","0","0","6","0","-2","0","0","0","3","0","-16","0","0","0","-21","0","4","0","0","0","-3","0","5","0","0","0","3","0","9","0","0","0","-15","0","-13","0","0","0","-15","0","-13","0","0","0","-3","0","20","0","0","0","-9","0","-12","0","0","0","9","0","-4","0","0","0","-12","0","2","0","0","0","-6","0","18","0","0","0","-15","0","11","0","0","0","-6","0","-4","0","0","0","3","0","9","0","0","0","12","0","17","0","0","0","3","0","-5","0","0","0","6","0","-1","0","0","0","-27","0","-13","0","0","0","6","0","-27","0","0","0","27","0","-1","0","0","0","18","0","4","0","0","0","-12","0","-9","0","0","0","9","0","-2","0","0","0","21","0","-18","0","0","0","6","0","8","0","0","0","-12","0","-1","0","0","0","-3","0","5","0","0","0","3","0","19","0","0","0","21","0","-9","0","0","0","-3","0","1","0","0","0","39","0","20","0","0","0","-21","0","-1","0","0","0","21","0","9","0","0","0","24","0","-4","0","0","0","-9","0","11","0","0","0","21","0","23","0","0","0","-15","0","13","0","0","0","-9","0","-1","0","0","0","-3","0","-36","0","0","0","0","0","-3","0","0","0","30","0","-13","0","0","0","-6","0","-1","0","0","0","3","0","-16","0","0","0","15","0","-9","0","0","0","-15","0","-18","0","0","0","-33","0","2","0","0","0","-3","0","-5","0","0","0","-6","0","23","0","0","0","-3","0","-27","0","0","0","-9","0","35","0","0","0","-24","0","13","0","0","0","-24","0","-34","0","0","0","-12","0","35","0","0","0","9","0","18","0","0","0","18","0","9","0","0","0","-3","0","-37","0","0","0","-3","0","-19","0","0","0","-12","0","7","0","0","0","3","0","-16","0","0","0","-27","0","-2","0","0","0","-33","0","32","0","0","0","3","0","18","0","0","0","-12","0","5","0","0","0","36","0","45","0","0","0","-39","0","10","0","0","0","21","0","-27","0","0","0","-42","0","8","0","0","0","-30","0","-14","0","0","0","3","0","36","0","0","0","18","0","-34","0","0","0","-6","0","-13","0","0","0","12","0","-11","0","0","0","30","0","1","0","0","0","-9","0","-27","0","0","0","-15","0","-31","0","0","0","12","0","-10","0","0","0","-9","0","-18","0","0","0","-15","0","-20","0","0","0","-6","0","-18","0","0","0","39","0","35","0","0","0","6","0","41","0","0","0","-9","0","26","0","0","0","-3","0","-13","0","0","0","6","0","-29","0","0","0","-12","0","-16","0","0","0","48","0","6","0","0","0","33","0","41","0","0","0","0","0","-9","0","0","0","21","0","63","0","0","0","21","0","11","0","0","0","-12","0","-9","0","0","0","39","0","11","0","0","0","-15","0","-11","0","0","0","36","0","9","0","0","0","-6","0","-1","0","0","0","-15","0","18","0","0","0","6","0","-8","0","0","0","15","0","-25","0","0","0","15","0","-9","0","0","0","0","0","7","0","0","0","-12","0","-37","0","0","0","6","0","23","0","0","0","21","0","-16","0","0","0","-9","0","45","0","0","0","12","0","-31","0","0","0","39","0","-10","0","0","0","-27","0","-2","0","0","0","-3","0","-1","0","0","0","-18","0","20","0","0","0","12","0","-36","0","0","0","39","0","-43","0","0","0","-9","0","13","0","0","0","9","0","-54","0","0","0","30","0","9","0","0","0","-6","0","20","0","0","0","-60","0","4","0","0","0","-51","0","-19","0","0","0","12","0","50","0","0","0","36","0","27","0","0","0","9","0","-20","0","0","0","36","0","2","0","0","0","6","0","-13","0","0","0","-27","0","41","0","0","0","-24","0","-27","0","0","0","-33","0","7","0","0","0","-3","0","23","0","0","0","-30","0","-4","0","0","0","-21","0","16","0","0","0","-36","0","36","0","0","0","-15","0","-36","0","0","0","-6","0","47","0","0","0","45","0","-27","0","0","0","21","0","-16","0","0","0","-12","0","8","0","0","0","-27","0","24","0","0","0","-54","0","-34","0","0","0","21","0","-9","0","0","0","-27","0","10","0","0","0","-54","0","45","0","0","0","3","0","-6","0","0","0","-33","0","-43","0","0","0","0","0","-5","0","0","0","57","0","18","0","0","0","-51","0","18","0","0","0","-3","0","8","0","0","0","12","0","-1","0","0","0"],"lmfdb":"agrees","curve":{"cremona":"324c1","lmfdb":"324.a","ainvs":[0,0,0,-9,9],"rank":1,"torsion":3}},{"label":"324.2.a.b","letter":"b","dim":1,"charpoly":["-68","1"],"traces":["1","0","0","0","-3","0","2","0","0","0","6","0","5","0","0","0","3","0","2","0","0","0","-6","0","4","0","0","0","-3","0","-4","0","0","0","-6","0","5","0","0","0","6","0","-10","0","0","0","0","0","-3","0","0","0","6","0","-18","0","0","0","12","0","5","0","0","0","-15","0","2","0","0","0","-6","0","-1","0","0","0","12","0","-10","0","0","0","0","0","-9","0","0","0","3","0","10","0","0","0","-6","0","-10","0","0","0","-6","0","-16","0","0","0","-12","0","-7","0","0","0","-9","0","18","0","0","0","6","0","25","0","0","0","3","0","2","0","0","0","6","0","4","0","0","0","15","0","8","0","0","0","30","0","9","0","0","0","-15","0","-4","0","0","0","12","0","5","0","0","0","-12","0","-4","0","0","0","-18","0","12","0","0","0","9","0","8","0","0","0","-12","0","14","0","0","0","-15","0","18","0","0","0","-6","0","-25","0","0","0","-15","0","20","0","0","0","-6","0","-18","0","0","0","12","0","14","0","0","0","30","0","-8","0","0","0","15","0","-10","0","0","0","-18","0","5","0","0","0","15","0","0","0","0","0","0","0","11","0","0","0","9","0","10","0","0","0","-30","0","-36","0","0","0","27","0","10","0","0","0","-24","0","-18","0","0","0","-3","0","-10","0","0","0","24","0","-10","0","0","0","15","0","-4","0","0","0","12","0","-8","0","0","0","-15","0","-36","0","0","0","-30","0","-20","0","0","0","-15","0","20","0","0","0","24","0","-25","0","0","0","-15","0","-18","0","0","0","6","0","20","0","0","0","0","0","26","0","0","0","-6","0","-10","0","0","0","-24","0","-20","0","0","0","18","0","2","0","0","0","-30","0","18","0","0","0","18","0","-15","0","0","0","3","0","32","0","0","0","12","0","14","0","0","0","-15","0","-4","0","0","0","-30","0","-36","0","0","0","30","0","-18","0","0","0","30","0","-7","0","0","0","15","0","-20","0","0","0","30","0","35","0","0","0","24","0","0","0","0","0","0","0","29","0","0","0","12","0","10","0","0","0","-24","0","11","0","0","0","-12","0","8","0","0","0","0","0","-9","0","0","0","-18","0","36","0","0","0","-30","0","35","0","0","0","6","0","-4","0","0","0","-12","0","4","0","0","0","-60","0","8","0","0","0","-18","0","25","0","0","0","30","0","20","0","0","0","-6","0","-9","0","0","0","-12","0","-22","0","0","0","0","0","18","0","0","0","6","0","-2","0","0","0","48","0","0","0","0","0","30","0","-10","0","0","0","-12","0","13","0","0","0","30","0","36","0","0","0","-18","0","41","0","0","0","21","0","-40","0","0","0","-6","0","-20","0","0","0","-15","0","-50","0","0","0","0","0","27","0","0","0","3","0","44","0","0","0","-24","0","-37","0","0","0","0","0","36","0","0","0","30","0","-8","0","0","0","39","0","-18","0","0","0","12","0","-1","0","0","0","-75","0","-10","0","0","0","0","0","-10","0","0","0","15","0","-40","0","0","0","6","0","-29","0","0","0","15","0","-4","0","0","0","-6","0","-15","0","0","0","-21","0","-40","0","0","0","-18","0","72","0","0","0","30","0","-18","0","0","0","-6","0","29","0","0","0","-12","0","18","0","0","0","30","0","-1","0","0","0","-42","0","-20","0","0","0","0","0","-45","0","0","0","30","0","-10","0","0","0","-24","0","18","0","0","0","-39","0","10","0","0","0","-12","0","-19","0","0","0","24","0","-90","0","0","0","-18","0","-32","0","0","0","-12","0","-10","0","0","0","-30","0","14","0","0","0","12","0","-52","0","0","0","36","0","45","0","0","0","-24","0","-10","0","0","0","12","0","-10","0","0","0","-9","0","-14","0","0","0","60","0","23","0","0","0","45","0","-16","0","0","0","12","0","-36","0","0","0","-15","0","38","0","0","0","-18","0","25","0","0","0","45","0","0","0","0","0","-6","0","36","0","0","0","3","0","-16","0","0","0","12","0","-20","0","0","0","21","0","-4","0","0","0","30","0","38","0","0","0","-9","0","54","0","0","0","18","0","-20","0","0","0","-36","0","50","0","0","0","-30","0","14","0","0","0","-45","0","8","0","0","0","-6","0","-27","0","0","0","-60","0","10","0","0","0","6","0","-55","0","0","0","6","0","-16","0","0","0","-30","0","4","0","0","0","0","0","36","0","0","0","12","0","18","0","0","0","-42","0","8","0","0","0","54","0","0","0","0","0","12","0","38","0","0","0","-30","0","20","0","0","0","27","0","-6","0","0","0","-54","0","23","0","0","0","-15","0","-36","0","0","0","-18","0","-5","0","0","0","-45","0","18","0","0","0","30","0","-15","0","0","0","75","0","38","0","0","0","54","0","16","0","0","0","30","0","18","0","0","0","-24","0","45","0","0","0","60","0","26","0","0","0","-60","0","53","0","0","0"],"lmfdb":"agrees","curve":{"cremona":"324d1","lmfdb":"324.b","ainvs":[0,0,0,-39,94],"rank":0,"torsion":3}},{"label":"324.2.a.c","letter":"c","dim":1,"charpoly":["-8","1"],"traces":["1","0","0","0","3","0","-1","0","0","0","3","0","-1","0","0","0","6","0","-4","0","0","0","-3","0","4","0","0","0","3","0","5","0","0","0","-3","0","2","0","0","0","3","0","-1","0","0","0","-9","0","-6","0","0","0","-6","0","9","0","0","0","-3","0","-13","0","0","0","-3","0","-7","0","0","0","-12","0","-10","0","0","0","-3","0","11","0","0","0","-9","0","18","0","0","0","6","0","1","0","0","0","-12","0","11","0","0","0","15","0","-7","0","0","0","12","0","2","0","0","0","-9","0","-9","0","0","0","-6","0","-2","0","0","0","-3","0","-16","0","0","0","21","0","4","0","0","0","3","0","5","0","0","0","-3","0","9","0","0","0","15","0","-13","0","0","0","15","0","-13","0","0","0","3","0","20","0","0","0","9","0","-12","0","0","0","-9","0","-4","0","0","0","12","0","2","0","0","0","6","0","18","0","0","0","15","0","11","0","0","0","6","0","-4","0","0","0","-3","0","9","0","0","0","-12","0","17","0","0","0","-3","0","-5","0","0","0","-6","0","-1","0","0","0","27","0","-13","0","0","0","-6","0","-27","0","0","0","-27","0","-1","0","0","0","-18","0","4","0","0","0","12","0","-9","0","0","0","-9","0","-2","0","0","0","-21","0","-18","0","0","0","-6","0","8","0","0","0","12","0","-1","0","0","0","3","0","5","0","0","0","-3","0","19","0","0","0","-21","0","-9","0","0","0","3","0","1","0","0","0","-39","0","20","0","0","0","21","0","-1","0","0","0","-21","0","9","0","0","0","-24","0","-4","0","0","0","9","0","11","0","0","0","-21","0","23","0","0","0","15","0","13","0","0","0","9","0","-1","0","0","0","3","0","-36","0","0","0","0","0","-3","0","0","0","-30","0","-13","0","0","0","6","0","-1","0","0","0","-3","0","-16","0","0","0","-15","0","-9","0","0","0","15","0","-18","0","0","0","33","0","2","0","0","0","3","0","-5","0","0","0","6","0","23","0","0","0","3","0","-27","0","0","0","9","0","35","0","0","0","24","0","13","0","0","0","24","0","-34","0","0","0","12","0","35","0","0","0","-9","0","18","0","0","0","-18","0","9","0","0","0","3","0","-37","0","0","0","3","0","-19","0","0","0","12","0","7","0","0","0","-3","0","-16","0","0","0","27","0","-2","0","0","0","33","0","32","0","0","0","-3","0","18","0","0","0","12","0","5","0","0","0","-36","0","45","0","0","0","39","0","10","0","0","0","-21","0","-27","0","0","0","42","0","8","0","0","0","30","0","-14","0","0","0","-3","0","36","0","0","0","-18","0","-34","0","0","0","6","0","-13","0","0","0","-12","0","-11","0","0","0","-30","0","1","0","0","0","9","0","-27","0","0","0","15","0","-31","0","0","0","-12","0","-10","0","0","0","9","0","-18","0","0","0","15","0","-20","0","0","0","6","0","-18","0","0","0","-39","0","35","0","0","0","-6","0","41","0","0","0","9","0","26","0","0","0","3","0","-13","0","0","0","-6","0","-29","0","0","0","12","0","-16","0","0","0","-48","0","6","0","0","0","-33","0","41","0","0","0","0","0","-9","0","0","0","-21","0","63","0","0","0","-21","0","11","0","0","0","12","0","-9","0","0","0","-39","0","11","0","0","0","15","0","-11","0","0","0","-36","0","9","0","0","0","6","0","-1","0","0","0","15","0","18","0","0","0","-6","0","-8","0","0","0","-15","0","-25","0","0","0","-15","0","-9","0","0","0","0","0","7","0","0","0","12","0","-37","0","0","0","-6","0","23","0","0","0","-21","0","-16","0","0","0","9","0","45","0","0","0","-12","0","-31","0","0","0","-39","0","-10","0","0","0","27","0","-2","0","0","0","3","0","-1","0","0","0","18","0","20","0","0","0","-12","0","-36","0","0","0","-39","0","-43","0","0","0","9","0","13","0","0","0","-9","0","-54","0","0","0","-30","0","9","0","0","0","6","0","20","0","0","0","60","0","4","0","0","0","51","0","-19","0","0","0","-12","0","50","0","0","0","-36","0","27","0","0","0","-9","0","-20","0","0","0","-36","0","2","0","0","0","-6","0","-13","0","0","0","27","0","41","0","0","0","24","0","-27","0","0","0","33","0","7","0","0","0","3","0","23","0","0","0","30","0","-4","0","0","0","21","0","16","0","0","0","36","0","36","0","0","0","15","0","-36","0","0","0","6","0","47","0","0","0","-45","0","-27","0","0","0","-21","0","-16","0","0","0","12","0","8","0","0","0","27","0","24","0","0","0","54","0","-34","0","0","0","-21","0","-9","0","0","0","27","0","10","0","0","0","54","0","45","0","0","0","-3","0","-6","0","0","0","33","0","-43","0","0","0","0","0","-5","0","0","0","-57","0","18","0","0","0","51","0","18","0","0","0","3","0","8","0","0","0","-12","0","-1","0","0","0"],"lmfdb":"agrees","curve":{"cremona":"324a1","lmfdb":"324.c","ainvs":[0,0,0,-21,37],"rank":0,"torsion":3}},{"label":"324.2.a.d","letter":"d","dim":1,"charpoly":["-14","1"],"traces":["1","0","0","0","3","0","2","0","0","0","-6","0","5","0","0","0","-3","0","2","0","0","0","6","0","4","0","0","0","3","0","-4","0","0","0","6","0","5","0","0","0","-6","0","-10","0","0","0","0","0","-3","0","0","0","-6","0","-18","0","0","0","-12","0","5","0","0","0","15","0","2","0","0","0","6","0","-1","0","0","0","-12","0","-10","0","0","0","0","0","-9","0","0","0","-3","0","10","0","0","0","6","0","-10","0","0","0","6","0","-16","0","0","0","12","0","-7","0","0","0","9","0","18","0","0","0","-6","0","25","0","0","0","-3","0","2","0","0","0","-6","0","4","0","0","0","-15","0","8","0","0","0","-30","0","9","0","0","0","15","0","-4","0","0","0","-12","0","5","0","0","0","12","0","-4","0","0","0","18","0","12","0","0","0","-9","0","8","0","0","0","12","0","14","0","0","0","15","0","18","0","0","0","6","0","-25","0","0","0","15","0","20","0","0","0","6","0","-18","0","0","0","-12","0","14","0","0","0","-30","0","-8","0","0","0","-15","0","-10","0","0","0","18","0","5","0","0","0","-15","0","0","0","0","0","0","0","11","0","0","0","-9","0","10","0","0","0","30","0","-36","0","0","0","-27","0","10","0","0","0","24","0","-18","0","0","0","3","0","-10","0","0","0","-24","0","-10","0","0","0","-15","0","-4","0","0","0","-12","0","-8","0","0","0","15","0","-36","0","0","0","30","0","-20","0","0","0","15","0","20","0","0","0","-24","0","-25","0","0","0","15","0","-18","0","0","0","-6","0","20","0","0","0","0","0","26","0","0","0","6","0","-10","0","0","0","24","0","-20","0","0","0","-18","0","2","0","0","0","30","0","18","0","0","0","-18","0","-15","0","0","0","-3","0","32","0","0","0","-12","0","14","0","0","0","15","0","-4","0","0","0","30","0","-36","0","0","0","-30","0","-18","0","0","0","-30","0","-7","0","0","0","-15","0","-20","0","0","0","-30","0","35","0","0","0","-24","0","0","0","0","0","0","0","29","0","0","0","-12","0","10","0","0","0","24","0","11","0","0","0","12","0","8","0","0","0","0","0","-9","0","0","0","18","0","36","0","0","0","30","0","35","0","0","0","-6","0","-4","0","0","0","12","0","4","0","0","0","60","0","8","0","0","0","18","0","25","0","0","0","-30","0","20","0","0","0","6","0","-9","0","0","0","12","0","-22","0","0","0","0","0","18","0","0","0","-6","0","-2","0","0","0","-48","0","0","0","0","0","-30","0","-10","0","0","0","12","0","13","0","0","0","-30","0","36","0","0","0","18","0","41","0","0","0","-21","0","-40","0","0","0","6","0","-20","0","0","0","15","0","-50","0","0","0","0","0","27","0","0","0","-3","0","44","0","0","0","24","0","-37","0","0","0","0","0","36","0","0","0","-30","0","-8","0","0","0","-39","0","-18","0","0","0","-12","0","-1","0","0","0","75","0","-10","0","0","0","0","0","-10","0","0","0","-15","0","-40","0","0","0","-6","0","-29","0","0","0","-15","0","-4","0","0","0","6","0","-15","0","0","0","21","0","-40","0","0","0","18","0","72","0","0","0","-30","0","-18","0","0","0","6","0","29","0","0","0","12","0","18","0","0","0","-30","0","-1","0","0","0","42","0","-20","0","0","0","0","0","-45","0","0","0","-30","0","-10","0","0","0","24","0","18","0","0","0","39","0","10","0","0","0","12","0","-19","0","0","0","-24","0","-90","0","0","0","18","0","-32","0","0","0","12","0","-10","0","0","0","30","0","14","0","0","0","-12","0","-52","0","0","0","-36","0","45","0","0","0","24","0","-10","0","0","0","-12","0","-10","0","0","0","9","0","-14","0","0","0","-60","0","23","0","0","0","-45","0","-16","0","0","0","-12","0","-36","0","0","0","15","0","38","0","0","0","18","0","25","0","0","0","-45","0","0","0","0","0","6","0","36","0","0","0","-3","0","-16","0","0","0","-12","0","-20","0","0","0","-21","0","-4","0","0","0","-30","0","38","0","0","0","9","0","54","0","0","0","-18","0","-20","0","0","0","36","0","50","0","0","0","30","0","14","0","0","0","45","0","8","0","0","0","6","0","-27","0","0","0","60","0","10","0","0","0","-6","0","-55","0","0","0","-6","0","-16","0","0","0","30","0","4","0","0","0","0","0","36","0","0","0","-12","0","18","0","0","0","42","0","8","0","0","0","-54","0","0","0","0","0","-12","0","38","0","0","0","30","0","20","0","0","0","-27","0","-6","0","0","0","54","0","23","0","0","0","15","0","-36","0","0","0","18","0","-5","0","0","0","45","0","18","0","0","0","-30","0","-15","0","0","0","-75","0","38","0","0","0","-54","0","16","0","0","0","-30","0","18","0","0","0","24","0","45","0","0","0","-60","0","26","0","0","0","60","0","53","0","0","0"],"lmfdb":"agrees","curve":{"cremona":"324b1","lmfdb":"324.d","ainvs":[0,0,0,9,-18],"rank":0,"torsion":3}}],"seconds":0.234,"computed":"atlas","estimate":{"seconds":0.393,"low":0.24,"high":0.68,"bytes":1990639}}