{"label":"50.2.a","level":50,"weight":2,"dims":{"new":2,"cusp":2,"eisenstein":11,"modsym":15},"old":[],"T":[[3,1],[7,1]],"status":"proven","checks":["dim M^+ at levels [1, 2, 5, 10, 25, 50]: [0, 1, 1, 3, 3, 9] (certified at ell = 2147482921)","T = [(3, 1), (7, 1)]; h of degree 2 = 1 x 2 (phi(ord eps) x dim S_k^new); 1 primes, 0 rejected"],"newforms":[{"label":"50.2.a.a","letter":"a","dim":1,"charpoly":["-3","1"],"traces":["1","-1","1","1","0","-1","2","-1","-2","0","-3","1","-4","-2","0","1","-3","2","5","0","2","3","6","-1","0","4","-5","2","0","0","2","-1","-3","3","0","-2","2","-5","-4","0","-3","-2","-4","-3","0","-6","12","1","-3","0","-3","-4","6","5","0","-2","5","0","0","0","2","-2","-4","1","0","3","-13","-3","6","0","12","2","11","-2","0","5","-6","4","-10","0","1","3","-9","2","0","4","0","3","15","0","-8","6","2","-12","0","-1","2","3","6","0","-18","3","-4","4","0","-6","-3","-5","-10","0","2","2","-9","-5","0","0","8","0","-6","0","-2","-2","-3","2","0","4","2","-1","-4","0","12","-3","10","13","0","3","-3","-6","5","0","12","-12","12","-2","0","-11","-3","2","0","0","2","-5","6","6","0","-4","2","10","6","0","12","-1","11","-3","0","9","12","-2","3","0","-10","-4","-24","0","0","-3","0","-15","-15","0","2","8","2","-6","0","-2","9","12","-10","0","-18","1","-19","-2","0","-3","-18","-6","20","0","-13","18","0","-3","0","4","-12","-4","-15","0","-13","6","12","3","0","5","4","10","11","0","12","-2","-4","-2","0","9","12","5","20","0","-6","0","6","-8","0","0","-10","6","0","0","17","2","16","2","0","3","-20","-2","-9","0","27","-4","-18","-2","0","1","-18","4","4","0","0","-12","6","3","0","-10","15","-13","0","0","2","-3","-8","3","0","6","32","-5","-4","0","-18","-12","11","12","0","-12","-6","2","-8","0","2","11","6","3","0","-2","15","0","-24","0","-8","-2","-18","5","0","-6","17","-6","-4","0","-18","4","26","-2","0","-10","12","-6","0","0","-3","-12","-15","1","0","-11","-10","3","24","0","17","-9","-4","-12","0","2","-13","-3","-9","0","-6","10","-20","4","0","24","-3","0","-10","0","20","3","6","0","0","15","-6","15","30","0","6","-2","-2","-8","0","-2","-28","6","6","0","12","2","26","-9","0","-12","0","10","-25","0","2","18","6","-1","0","19","8","2","30","0","-18","3","12","18","0","6","-28","-20","10","0","-3","13","-8","-18","0","0","-6","3","5","0","-3","-4","0","12","0","4","5","15","-15","0","-28","13","-24","-6","0","-12","4","-3","12","0","-18","-5","-19","-4","0","-10","30","-11","-40","0","6","-12","-9","2","0","4","0","2","-15","0","9","-9","2","-12","0","-5","17","-20","15","0","12","6","-4","0","0","-6","12","8","-26","0","2","0","12","10","0","-6","-12","0","30","0","-8","-17","12","-2","0","-16","2","-2","11","0","12","-3","0","20","0","2","24","9","20","0","12","-27","36","4","0","18","3","2","-30","0","22","-1","-25","18","0","-4","-36","-4","-24","0","-3","0","41","12","0","-6","-6","-3","13","0","0","10","12","-15","0","13","-15","0","9","0","32","-2","2","3","0","8","17","-3","-4","0","0","-6","-20","-32","0","5","12","4","16","0","9","18","-24","12","0","-11","2","-12","-15","0","-28","12","-18","6","0","-2","-13","8","-19","0","-18","-2","-18","-11","0","-6","-33","-3","10","0","-18","2","-9","-15","0","0","20","24","30","0","-13","8","26","2","0","18","32","-5","0","0","-48","6","-34","-17","0","6","-18","4","20","0","-30","18","30","-4","0","-26","-15","2","-6","0","2","10","-13","-12","0","6","12","0","-24","0","42","3","-4","12","0","15","12","-1","0","0","4","11","6","10","0","-3","-22","-24","15","0","32","-17","12","9","0","4","0","12","-4","0","-6","-2","26","13","0","3","-48","9","4","0","12","6","-39","-10","0","20","20","-4","-24","0","17","-24","12","3","0","0","9","10","6","0","12","-20","10","-3","0","-6","-36","0","20","0","20","-15","12","6","0","-15","0","-30","-30","0","-8","-6","17","2","0","2","32","8","13","0","12","2","-4","28","0","-6","39","-6","20","0","-20","-12","6","-2","0","-26","18","9","-6","0","32","12","27","0","0","-10","32","25","-18","0","-3","-2","-20","-18","0","-6","0","1","5","0","-18","-19","-24","-8","0","-2","4","-30","-15","0","-36","18","0","-3","0","-12","-28","-18","6","0","-18","-6","-8","28","0","20","42","-10","-36","0","-30","3","-33","-13","0","8","0","18","-30","0","-28","0","2","6","0","-3","-20","-5","16","0","42","3","-4","4","0","0","-33","-12","20","0","32","-4","9","-5","0","-15","-10","15","0","0","-29","28","-18","-13","0","24","-4","6","11","0","12","12","26","-4","0","3","-3","-12","5","0","-6","18","-24","5","0","19","-8","4","30","0","52","10","-4","-30","0","11","-28","40","6","0","-18","-6","41","12","0","9","12","-2","4","0","-3","-4","60","0","0","-2","-24","15","0","0","-18","-9","-8","9","0","-2","-28","12","36","0","12","5","27","-17","0","20","24","-15","-10","0","17","-12","-48","-6","0","4","8","0","30","0","-15","6","-18","-12","0","-8","-13","26","26","0","12","-2","-18","0","0","-12","-48","-10","-44","0","12","6","-39","12","0","0","0","-30","-6","0","-27","8","6","17","0","-12","32","2","-15","0","-3","16","10","-2","0","2","57","-11","-45","0","20","-12","6","3","0","0","24","-20","-24","0","-58","-2","17","-24","0","-9","-28","-20","-10","0"],"lmfdb":"agrees","curve":{"cremona":"50a1","lmfdb":"50.a","ainvs":[1,0,1,-1,-2],"rank":0,"torsion":3},"derived":{"al":[[2,1],[5,null]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"50.2.a.b","letter":"b","dim":1,"charpoly":["3","1"],"traces":["1","1","-1","1","0","-1","-2","1","-2","0","-3","-1","4","-2","0","1","3","-2","5","0","2","-3","-6","-1","0","4","5","-2","0","0","2","1","3","3","0","-2","-2","5","-4","0","-3","2","4","-3","0","-6","-12","-1","-3","0","-3","4","-6","5","0","-2","-5","0","0","0","2","2","4","1","0","3","13","3","6","0","12","-2","-11","-2","0","5","6","-4","-10","0","1","-3","9","2","0","4","0","-3","15","0","-8","-6","-2","-12","0","-1","-2","-3","6","0","-18","-3","4","4","0","-6","3","5","-10","0","2","-2","9","-5","0","0","-8","0","-6","0","-2","2","3","2","0","4","-2","1","-4","0","12","3","-10","13","0","3","3","6","5","0","12","12","-12","-2","0","-11","3","-2","0","0","2","5","-6","6","0","-4","-2","-10","6","0","12","1","-11","-3","0","9","-12","2","3","0","-10","4","24","0","0","-3","0","15","-15","0","2","-8","-2","-6","0","-2","-9","-12","-10","0","-18","-1","19","-2","0","-3","18","6","20","0","-13","-18","0","-3","0","4","12","4","-15","0","-13","-6","-12","3","0","5","-4","-10","11","0","12","2","4","-2","0","9","-12","-5","20","0","-6","0","-6","-8","0","0","10","-6","0","0","17","-2","-16","2","0","3","20","2","-9","0","27","4","18","-2","0","1","18","-4","4","0","0","12","-6","3","0","-10","-15","13","0","0","2","3","8","3","0","6","-32","5","-4","0","-18","12","-11","12","0","-12","6","-2","-8","0","2","-11","-6","3","0","-2","-15","0","-24","0","-8","2","18","5","0","-6","-17","6","-4","0","-18","-4","-26","-2","0","-10","-12","6","0","0","-3","12","15","1","0","-11","10","-3","24","0","17","9","4","-12","0","2","13","3","-9","0","-6","-10","20","4","0","24","3","0","-10","0","20","-3","-6","0","0","15","6","-15","30","0","6","2","2","-8","0","-2","28","-6","6","0","12","-2","-26","-9","0","-12","0","-10","-25","0","2","-18","-6","-1","0","19","-8","-2","30","0","-18","-3","-12","18","0","6","28","20","10","0","-3","-13","8","-18","0","0","6","-3","5","0","-3","4","0","12","0","4","-5","-15","-15","0","-28","-13","24","-6","0","-12","-4","3","12","0","-18","5","19","-4","0","-10","-30","11","-40","0","6","12","9","2","0","4","0","-2","-15","0","9","9","-2","-12","0","-5","-17","20","15","0","12","-6","4","0","0","-6","-12","-8","-26","0","2","0","-12","10","0","-6","12","0","30","0","-8","17","-12","-2","0","-16","-2","2","11","0","12","3","0","20","0","2","-24","-9","20","0","12","27","-36","4","0","18","-3","-2","-30","0","22","1","25","18","0","-4","36","4","-24","0","-3","0","-41","12","0","-6","6","3","13","0","0","-10","-12","-15","0","13","15","0","9","0","32","2","-2","3","0","8","-17","3","-4","0","0","6","20","-32","0","5","-12","-4","16","0","9","-18","24","12","0","-11","-2","12","-15","0","-28","-12","18","6","0","-2","13","-8","-19","0","-18","2","18","-11","0","-6","33","3","10","0","-18","-2","9","-15","0","0","-20","-24","30","0","-13","-8","-26","2","0","18","-32","5","0","0","-48","-6","34","-17","0","6","18","-4","20","0","-30","-18","-30","-4","0","-26","15","-2","-6","0","2","-10","13","-12","0","6","-12","0","-24","0","42","-3","4","12","0","15","-12","1","0","0","4","-11","-6","10","0","-3","22","24","15","0","32","17","-12","9","0","4","0","-12","-4","0","-6","2","-26","13","0","3","48","-9","4","0","12","-6","39","-10","0","20","-20","4","-24","0","17","24","-12","3","0","0","-9","-10","6","0","12","20","-10","-3","0","-6","36","0","20","0","20","15","-12","6","0","-15","0","30","-30","0","-8","6","-17","2","0","2","-32","-8","13","0","12","-2","4","28","0","-6","-39","6","20","0","-20","12","-6","-2","0","-26","-18","-9","-6","0","32","-12","-27","0","0","-10","-32","-25","-18","0","-3","2","20","-18","0","-6","0","-1","5","0","-18","19","24","-8","0","-2","-4","30","-15","0","-36","-18","0","-3","0","-12","28","18","6","0","-18","6","8","28","0","20","-42","10","-36","0","-30","-3","33","-13","0","8","0","-18","-30","0","-28","0","-2","6","0","-3","20","5","16","0","42","-3","4","4","0","0","33","12","20","0","32","4","-9","-5","0","-15","10","-15","0","0","-29","-28","18","-13","0","24","4","-6","11","0","12","-12","-26","-4","0","3","3","12","5","0","-6","-18","24","5","0","19","8","-4","30","0","52","-10","4","-30","0","11","28","-40","6","0","-18","6","-41","12","0","9","-12","2","4","0","-3","4","-60","0","0","-2","24","-15","0","0","-18","9","8","9","0","-2","28","-12","36","0","12","-5","-27","-17","0","20","-24","15","-10","0","17","12","48","-6","0","4","-8","0","30","0","-15","-6","18","-12","0","-8","13","-26","26","0","12","2","18","0","0","-12","48","10","-44","0","12","-6","39","12","0","0","0","30","-6","0","-27","-8","-6","17","0","-12","-32","-2","-15","0","-3","-16","-10","-2","0","2","-57","11","-45","0","20","12","-6","3","0","0","-24","20","-24","0","-58","2","-17","-24","0","-9","28","20","-10","0"],"lmfdb":"agrees","curve":{"cremona":"50b1","lmfdb":"50.b","ainvs":[1,1,1,-3,1],"rank":0,"torsion":5},"derived":{"al":[[2,-1],[5,null]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.089,"computed":"atlas","estimate":{"seconds":0.209,"low":0.127,"high":0.361,"bytes":1823872},"url":"https://sagebrush.space/atlas/mf/50.2.a"}