{"label":"772.2.a","level":772,"weight":2,"dims":{"new":16,"cusp":95,"eisenstein":5,"modsym":195},"old":[[193,15,3],[386,17,2]],"T":[[3,1],[5,3]],"status":"proven","checks":["dim M^+ at levels [1, 2, 4, 193, 386, 772]: [0, 1, 2, 16, 50, 100] (certified at ell = 2147483137)","T = [(3, 1), (5, 3)]; h of degree 16 = 1 x 16 (phi(ord eps) x dim S_k^new); 3 primes, 0 rejected"],"newforms":[{"label":"772.2.a.a","letter":"a","dim":2,"charpoly":["16","12","1"],"traces":["2","0","0","0","-4","0","1","0","4","0","-1","0","-10","0","-10","0","-6","0","-4","0","5","0","7","0","8","0","0","0","3","0","3","0","-25","0","-7","0","7","0","0","0","-5","0","-17","0","-8","0","-13","0","-11","0","-10","0","-14","0","27","0","-10","0","-12","0","-1","0","2","0","20","0","-5","0","5","0","18","0","22","0","40","0","-13","0","13","0","-22","0","-27","0","22","0","25","0","-7","0","-5","0","15","0","18","0","-18","0","-2","0","-20","0","0","0","-15","0","0","0","14","0","15","0","5","0","-19","0","-20","0","-8","0","41","0","25","0","-36","0","20","0","15","0","3","0","-7","0","10","0","0","0","-3","0","-5","0","5","0","-31","0","5","0","0","0","-7","0","-12","0","-21","0","-4","0","10","0","6","0","14","0","55","0","27","0","24","0","-8","0","15","0","24","0","0","0","4","0","-1","0","-5","0","-29","0","28","0","-5","0","-10","0","2","0","50","0","-39","0","-30","0","5","0","14","0","-15","0","14","0","27","0","24","0","-30","0","19","0","9","0","10","0","30","0","-46","0","16","0","21","0","2","0","-15","0","-12","0","31","0","-35","0","-8","0","-3","0","0","0","17","0","20","0","5","0","-21","0","-16","0","50","0","-9","0","11","0","6","0","18","0","18","0","-35","0","24","0","-17","0","-25","0","-104","0","12","0","6","0","-25","0","-34","0","40","0","10","0","-6","0","-30","0","24","0","24","0","25","0","-35","0","-1","0","-10","0","7","0","24","0","30","0","24","0","-44","0","-14","0","-27","0","-64","0","70","0","22","0","-40","0","10","0","-9","0","-42","0","14","0","5","0","16","0","-5","0","-39","0","-10","0","-45","0","-21","0","4","0","0","0","-13","0","-6","0","-20","0","32","0","-20","0","25","0","-54","0","-19","0","-10","0","-2","0","1","0","-70","0","-15","0","50","0","-10","0","2","0","41","0","-34","0","-45","0","-26","0","15","0","9","0","46","0","-15","0","-9","0","-15","0","44","0","-41","0","-5","0","-20","0","-6","0","49","0","45","0","35","0","25","0","-26","0","-64","0","-3","0","125","0","-28","0","4","0","-65","0","-19","0","21","0","-22","0","30","0","49","0","-30","0","42","0","-60","0","-65","0","35","0","8","0","10","0","-37","0","4","0","-45","0","-26","0","0","0","-40","0","-29","0","-56","0","-28","0","45","0","-35","0","20","0","66","0","30","0","0","0","36","0","-34","0","54","0","-6","0","12","0","-15","0","78","0","50","0","0","0","12","0","16","0","10","0","-30","0","19","0","45","0","-46","0","50","0","40","0","-24","0","-19","0","-24","0","25","0","-70","0","-40","0","-7","0","-44","0","-45","0","-38","0","-9","0","-2","0","-31","0","-11","0","-65","0","9","0","85","0","80","0","-11","0","-5","0","-11","0","-40","0","0","0","80","0","48","0","53","0","0","0","-11","0","-18","0","40","0","-46","0","-21","0","-5","0","-45","0","36","0","0","0","6","0","26","0","-10","0","-107","0","-1","0","20","0","65","0","10","0","-25","0","-22","0","20","0","-5","0","-21","0","102","0","55","0","-36","0","2","0","-60","0","-30","0","55","0","36","0","0","0","-30","0","55","0","-22","0","6","0","15","0","-54","0","-21","0","44","0","-14","0","4","0","50","0","29","0","23","0","-20","0","13","0","14","0","-40","0","39","0","-24","0","-5","0","-62","0","20","0","70","0","70","0","-12","0","-26","0","-39","0","-10","0","40","0","15","0","-29","0","75","0","-15","0","9","0","26","0","18","0","-135","0","-40","0","53","0","15","0","-45","0","112","0","24","0","-14","0","36","0","14","0","45","0","-10","0","31","0","50","0","-8","0","30","0","-54","0","35","0","-33","0","15","0","79","0","-40","0","-90","0","70","0","12","0","44","0","60","0","36","0","5","0","1","0","72","0","25","0","-15","0","66","0","-25","0","48","0","-84","0","-20","0","0","0","5","0","50","0","-15","0","44","0","-14","0","-36","0","-32","0","70","0","50","0","-20","0","-45","0","-28","0","19","0","-10","0","-6","0","-43","0","-120","0","24","0","37","0","-30","0","28","0","-39","0","-15","0","70","0","9","0","-35","0","-48","0","33","0","40","0","32","0","10","0","36","0","-42","0","-68","0","0","0","-48","0","-75","0","60","0","81","0","25","0","-36","0","-53","0","-46","0","30","0","-30","0","2","0","60","0","-39","0","5","0","11","0","31","0","32","0","-25","0","42","0","32","0","-35","0","47","0","34","0","-40","0","36","0","1","0","15","0","9","0","-35","0","-30","0","-90","0","88","0","0","0","-63","0","17","0","-90","0","-136","0","41","0","10","0","-3","0","-5","0","15","0","6","0","-110","0","5","0","24","0","-60","0","-50","0","-10","0","-35","0","0","0","-4","0","13","0","50","0","45","0","21","0","-200","0","-66","0","91","0","28","0","78","0","83","0","-35","0","-52","0","-40","0","0","0","60","0","-26","0","-15","0"],"lmfdb":"agrees"},{"label":"772.2.a.b","letter":"b","dim":5,"charpoly":["-1091","-2413","-554","57","21","1"],"traces":["5","0","-3","0","-6","0","0","0","0","0","-6","0","4","0","13","0","-17","0","-2","0","-19","0","-8","0","1","0","-21","0","-15","0","-2","0","0","0","-14","0","-22","0","-8","0","-16","0","17","0","-33","0","5","0","7","0","11","0","-12","0","-7","0","-1","0","8","0","-15","0","29","0","-33","0","14","0","14","0","1","0","-21","0","-43","0","-9","0","2","0","49","0","-1","0","19","0","13","0","-23","0","9","0","-32","0","15","0","13","0","34","0","-1","0","-6","0","48","0","7","0","18","0","41","0","-28","0","14","0","36","0","30","0","-21","0","-3","0","-12","0","20","0","-4","0","-13","0","-1","0","85","0","-31","0","22","0","-10","0","20","0","46","0","8","0","-10","0","22","0","-31","0","4","0","-4","0","16","0","-37","0","-34","0","22","0","30","0","-11","0","-5","0","-43","0","45","0","-5","0","0","0","26","0","66","0","11","0","-9","0","-8","0","42","0","5","0","52","0","29","0","46","0","-18","0","-36","0","35","0","5","0","-7","0","-15","0","-21","0","-5","0","45","0","35","0","-10","0","36","0","123","0","-67","0","-9","0","-7","0","-11","0","-20","0","37","0","32","0","3","0","-71","0","-15","0","-29","0","17","0","-32","0","33","0","-76","0","-31","0","-13","0","-4","0","-65","0","11","0","28","0","-46","0","23","0","-48","0","37","0","6","0","53","0","15","0","-31","0","-8","0","30","0","54","0","-32","0","-60","0","-41","0","-63","0","-6","0","-35","0","4","0","57","0","14","0","7","0","-32","0","-34","0","-90","0","-14","0","22","0","6","0","-33","0","40","0","-1","0","5","0","-22","0","-55","0","8","0","-9","0","58","0","-11","0","-39","0","-25","0","-49","0","93","0","-100","0","-53","0","-39","0","76","0","-17","0","-17","0","2","0","19","0","-22","0","-8","0","-58","0","-83","0","103","0","-64","0","40","0","79","0","-17","0","6","0","1","0","1","0","22","0","15","0","-24","0","-33","0","46","0","-16","0","-38","0","-153","0","27","0","-43","0","-24","0","-35","0","11","0","23","0","-46","0","-12","0","30","0","-54","0","-93","0","-28","0","34","0","11","0","-47","0","-84","0","-15","0","9","0","-41","0","53","0","3","0","-33","0","-14","0","57","0","-28","0","7","0","180","0","58","0","-11","0","81","0","47","0","7","0","-58","0","-7","0","28","0","35","0","-72","0","41","0","-25","0","11","0","-8","0","67","0","-37","0","-15","0","-58","0","1","0","-24","0","-50","0","-15","0","62","0","-9","0","26","0","-35","0","1","0","19","0","10","0","46","0","-2","0","-101","0","-71","0","-18","0","77","0","67","0","-57","0","-32","0","-44","0","25","0","97","0","-63","0","11","0","41","0","-117","0","42","0","-11","0","-140","0","-48","0","-11","0","49","0","9","0","42","0","102","0","19","0","-94","0","-29","0","-47","0","-9","0","-3","0","35","0","67","0","-89","0","-69","0","66","0","-100","0","32","0","50","0","4","0","35","0","-54","0","-3","0","52","0","47","0","63","0","25","0","46","0","-37","0","-39","0","9","0","23","0","1","0","49","0","-24","0","107","0","33","0","-22","0","53","0","31","0","98","0","50","0","-89","0","39","0","92","0","57","0","3","0","-53","0","6","0","-26","0","23","0","-21","0","59","0","-1","0","70","0","82","0","15","0","37","0","-217","0","-82","0","55","0","-29","0","79","0","78","0","34","0","6","0","3","0","59","0","5","0","62","0","-89","0","60","0","16","0","50","0","-31","0","16","0","-82","0","-66","0","15","0","9","0","84","0","110","0","44","0","-5","0","73","0","159","0","-84","0","-13","0","15","0","-39","0","20","0","6","0","78","0","-53","0","-94","0","12","0","-86","0","44","0","19","0","30","0","27","0","-7","0","-59","0","260","0","69","0","112","0","40","0","-39","0","101","0","136","0","64","0","56","0","53","0","27","0","-30","0","46","0","-9","0","-33","0","-5","0","24","0","-72","0","-69","0","44","0","50","0","-34","0","-29","0","53","0","15","0","185","0","-48","0","86","0","-78","0","7","0","-94","0","-11","0","109","0","-18","0","-8","0","-77","0","-33","0","3","0","12","0","-55","0","43","0","45","0","-4","0","-70","0","-13","0","-38","0","-38","0","34","0","96","0","-25","0","75","0","-89","0","-8","0","-48","0","-9","0","-60","0","84","0","-19","0","52","0","-31","0","88","0","9","0","-104","0","38","0","79","0","-70","0","17","0","52","0","-69","0","-97","0","-119","0","2","0","-40","0","31","0","-60","0","-213","0","-19","0","-7","0","-31","0","56","0","-62","0","-132","0","-112","0","-136","0","-2","0","108","0","12","0","28","0","-51","0","-53","0","168","0","11","0","18","0","11","0","43","0","-137","0","-6","0","75","0","-3","0","-19","0","-6","0","35","0","65","0","-1","0","-76","0","-167","0","100","0","-13","0","-3","0","-61","0","-178","0","2","0","106","0","88","0","-25","0","39","0","-47","0","121","0"],"lmfdb":"agrees"},{"label":"772.2.a.c","letter":"c","dim":9,"charpoly":["23946128","5005696","-5070568","15516","334213","-52533","380","505","-41","1"],"traces":["9","0","5","0","12","0","1","0","14","0","7","0","8","0","3","0","17","0","4","0","2","0","-1","0","23","0","11","0","10","0","1","0","11","0","-1","0","15","0","-8","0","15","0","16","0","25","0","-8","0","6","0","-1","0","14","0","-12","0","5","0","12","0","2","0","-1","0","15","0","-11","0","-9","0","-1","0","7","0","1","0","6","0","-13","0","13","0","12","0","13","0","-10","0","12","0","-26","0","-5","0","-11","0","19","0","-14","0","19","0","-30","0","-25","0","7","0","-48","0","-22","0","37","0","-45","0","-12","0","-28","0","-6","0","-22","0","42","0","-20","0","-41","0","6","0","-16","0","5","0","37","0","-49","0","-31","0","-15","0","-17","0","-23","0","-8","0","-41","0","-25","0","-45","0","0","0","-64","0","13","0","-30","0","-35","0","-13","0","-37","0","-29","0","8","0","-51","0","7","0","-12","0","-23","0","-65","0","42","0","-9","0","-77","0","-12","0","-9","0","-26","0","34","0","-60","0","35","0","16","0","0","0","-81","0","8","0","25","0","43","0","2","0","-34","0","-5","0","40","0","-30","0","29","0","52","0","-19","0","-10","0","55","0","-53","0","-30","0","-8","0","0","0","33","0","94","0","7","0","-62","0","47","0","-15","0","-50","0","48","0","-70","0","64","0","-49","0","25","0","33","0","18","0","-48","0","-25","0","49","0","2","0","-65","0","36","0","21","0","-100","0","-8","0","2","0","50","0","72","0","7","0","46","0","19","0","12","0","30","0","20","0","-20","0","-27","0","28","0","-6","0","56","0","11","0","-66","0","36","0","121","0","30","0","-51","0","26","0","24","0","13","0","-23","0","-5","0","75","0","64","0","-25","0","-40","0","4","0","-57","0","0","0","106","0","67","0","24","0","27","0","-19","0","39","0","25","0","-21","0","-28","0","58","0","24","0","7","0","69","0","-30","0","-31","0","45","0","-17","0","59","0","-12","0","72","0","66","0","121","0","11","0","51","0","43","0","23","0","31","0","2","0","0","0","136","0","47","0","22","0","-36","0","49","0","43","0","42","0","70","0","88","0","-23","0","40","0","-51","0","28","0","83","0","-40","0","-51","0","121","0","-46","0","-31","0","13","0","98","0","60","0","-25","0","55","0","-24","0","41","0","-11","0","50","0","89","0","-121","0","138","0","54","0","-8","0","-53","0","-43","0","6","0","143","0","75","0","10","0","-141","0","19","0","-9","0","-52","0","-47","0","146","0","-119","0","-31","0","-50","0","35","0","32","0","39","0","-43","0","-75","0","-27","0","-97","0","54","0","9","0","-187","0","-30","0","-60","0","103","0","56","0","66","0","-108","0","50","0","-53","0","20","0","-111","0","-40","0","-63","0","-101","0","24","0","63","0","5","0","-106","0","-71","0","102","0","5","0","-121","0","-89","0","50","0","-81","0","-143","0","-12","0","-5","0","40","0","65","0","-109","0","33","0","-45","0","107","0","-17","0","-98","0","-8","0","-95","0","-4","0","95","0","-95","0","46","0","-119","0","74","0","-60","0","-166","0","11","0","33","0","-126","0","-142","0","33","0","-5","0","15","0","17","0","-30","0","-5","0","-38","0","-26","0","-54","0","113","0","-94","0","62","0","-135","0","70","0","-13","0","71","0","-28","0","-97","0","3","0","53","0","-68","0","-23","0","-174","0","-132","0","-33","0","139","0","61","0","51","0","52","0","57","0","-44","0","-120","0","-36","0","83","0","39","0","-150","0","32","0","-89","0","-63","0","-13","0","-203","0","46","0","-7","0","116","0","36","0","-6","0","-27","0","-17","0","-47","0","135","0","-7","0","-61","0","-133","0","60","0","-29","0","-60","0","-49","0","-29","0","36","0","-42","0","-59","0","-36","0","-161","0","89","0","-119","0","40","0","-50","0","-17","0","-33","0","77","0","-120","0","-127","0","-36","0","89","0","166","0","-35","0","101","0","49","0","-26","0","34","0","95","0","32","0","-96","0","39","0","28","0","-39","0","-7","0","-36","0","-39","0","-8","0","32","0","84","0","-29","0","7","0","-42","0","-19","0","41","0","-60","0","-12","0","20","0","-94","0","-59","0","-20","0","-40","0","40","0","56","0","40","0","-39","0","59","0","264","0","-41","0","38","0","-42","0","-10","0","13","0","-278","0","72","0","-6","0","-6","0","-59","0","-188","0","43","0","1","0","123","0","199","0","-215","0","48","0","-81","0","-34","0","-63","0","234","0","-116","0","-67","0","133","0","2","0","-42","0","16","0","-4","0","-49","0","-40","0","-72","0","70","0","-84","0","-105","0","73","0","-82","0","146","0","14","0","-47","0","-26","0","52","0","12","0","-11","0","89","0","56","0","-92","0","-71","0","-10","0","42","0","22","0","-191","0","33","0","28","0","16","0","15","0","-27","0","-84","0","-103","0","-100","0","73","0","-12","0","20","0","151","0","-40","0","61","0","29","0","102","0","-66","0","-31","0","25","0","83","0","-61","0","-54","0","-54","0","187","0","-127","0","171","0","46","0"],"lmfdb":"agrees"}],"seconds":0.238,"computed":"atlas","estimate":{"seconds":0.493,"low":0.301,"high":0.853,"bytes":2172560}}