{"label":"30.2.a","level":30,"weight":2,"dims":{"new":1,"cusp":3,"eisenstein":7,"modsym":13},"old":[[15,1,2]],"T":[[7,1],[11,3]],"status":"proven","checks":["dim M^+ at levels [1, 2, 3, 5, 6, 10, 15, 30]: [0, 1, 1, 1, 3, 3, 4, 10] (certified at ell = 2147483629)","T = [(7, 1), (11, 3)]; h of degree 1 = 1 x 1 (phi(ord eps) x dim S_k^new); 1 primes, 0 rejected"],"newforms":[{"label":"30.2.a.a","letter":"a","dim":1,"charpoly":["4","1"],"traces":["1","-1","1","1","-1","-1","-4","-1","1","1","0","1","2","4","-1","1","6","-1","-4","-1","-4","0","0","-1","1","-2","1","-4","-6","1","8","-1","0","-6","4","1","2","4","2","1","-6","4","-4","0","-1","0","0","1","9","-1","6","2","-6","-1","0","4","-4","6","0","-1","-10","-8","-4","1","-2","0","-4","6","0","-4","0","-1","2","-2","1","-4","0","-2","8","-1","1","6","12","-4","-6","4","-6","0","18","1","-8","0","8","0","4","-1","2","-9","0","1","18","-6","-4","-2","4","6","-12","1","-10","0","2","-4","-18","4","0","-6","2","0","-24","1","-11","10","-6","8","-1","4","20","-1","-4","2","0","0","16","4","-1","-6","6","0","-4","4","0","0","0","1","6","-2","9","2","-6","-1","8","4","6","0","-8","2","2","-8","-6","1","0","-1","-4","-6","0","-12","0","4","-9","6","-4","-4","18","6","-4","0","0","-18","24","-1","14","8","-10","0","-2","-8","0","0","-4","-4","-24","1","-22","-2","-2","9","-6","0","8","-1","-4","-18","24","6","6","4","0","2","0","-4","20","-6","0","12","4","-1","-32","10","2","0","12","-2","20","4","1","18","-12","-4","-10","0","0","6","-18","-2","0","0","8","24","24","-1","2","11","1","-10","-9","6","-8","-8","12","1","-24","-4","0","-20","-6","1","-18","4","-8","-2","-6","0","0","0","6","-16","18","-4","-6","1","-16","6","-8","-6","0","0","2","4","8","-4","18","0","-28","0","4","0","24","-1","19","-6","2","2","-6","-9","0","-2","0","6","0","1","16","-8","18","-4","10","-6","20","0","-4","8","0","-2","2","-2","4","8","18","6","0","-1","-12","0","-24","1","2","4","-10","6","0","0","-28","12","2","0","4","-4","26","9","-18","-6","0","4","-8","4","0","-18","12","-6","-10","4","2","0","6","0","0","18","-24","-24","-24","1","-3","-14","-11","-8","-2","10","-28","0","-6","2","24","8","26","0","-1","0","-12","4","-4","4","20","24","0","-1","0","22","-4","2","-6","2","0","-9","0","6","-8","0","-22","-8","16","1","-6","4","16","18","-1","-24","0","-6","26","-6","6","-4","0","0","-12","-2","-4","0","0","4","-10","-20","0","6","6","0","40","-12","0","-4","0","1","26","32","6","-10","0","-2","8","0","9","-12","12","2","-18","-20","-6","-4","-6","-1","0","-18","8","12","8","4","26","10","6","0","-30","0","-4","-6","-8","18","-36","2","16","0","2","0","0","-8","-4","-24","-6","-24","-24","1","4","-2","0","-11","-2","-1","-28","10","-4","9","24","-6","-36","8","0","8","0","-12","-4","-1","0","24","24","4","-18","0","-9","20","-6","6","-8","-1","-4","18","4","-4","0","8","18","2","18","6","20","0","-4","0","48","0","-23","-6","0","16","-12","-18","12","4","24","6","0","-1","-10","16","14","-6","10","8","-28","6","-10","0","24","0","-32","-2","-2","-4","18","-8","-8","4","0","-18","-12","0","18","28","-4","0","18","-4","20","0","-24","-24","0","1","2","-19","-22","6","-48","-2","0","-2","-2","6","-12","9","-32","0","-6","2","30","0","24","-6","8","0","-24","-1","-22","-16","-4","8","11","-18","-4","4","24","-10","0","6","2","-20","6","0","30","4","44","-8","0","0","-72","2","1","-2","0","2","12","-4","32","-8","20","-18","-20","-6","18","0","0","1","-30","12","-4","0","4","24","24","-1","0","-2","-32","-4","18","10","0","-6","2","0","48","0","14","28","12","-12","-16","-2","0","0","20","-4","0","4","26","-26","1","-9","-6","18","-8","6","-12","0","-12","-4","-6","8","-10","-4","-12","0","44","18","0","-12","4","6","-36","10","-18","-4","-6","-2","-8","0","0","-6","-72","0","38","0","8","-18","0","24","0","24","24","24","0","-1","16","3","2","14","-6","11","-28","8","1","2","-24","-10","-22","28","-9","0","0","6","-52","-2","-8","-24","-24","-8","6","-26","12","0","48","1","-40","0","-24","12","-8","-4","2","4","0","-4","18","-20","40","-24","-6","0","0","1","2","0","-18","-22","42","4","8","-2","-8","6","24","-2","0","0","-6","9","-2","0","-4","-6","0","8","72","0","-20","22","6","8","-30","-16","0","-1","18","6","0","-4","0","-16","-6","-18","-54","1","-4","24","-16","0","4","6","16","-26","-8","6","18","-6","20","4","0","0","12","0","38","12","2","2","54","4","0","0","8","0","24","-4","7","10","18","20","9","0","44","-6","-28","-6","0","0","-46","-40","4","12","-18","0","-4","4","24","0","24","-1","-18","-26","19","-32","0","-6","-8","10","2","0","4","2","2","-8","-6","0","-54","-9","-4","12","0","-12","0","-2","-80","18","0","20","0","6","-24","4","0","6","-48","1","-36","0","16","18","-14","-8","44","-12","18","-8","-48","-4","0","-26","10","-10","0","-6","-16","0","20","30","0","0","2","4","-4","6","-6","8","-36","-18","0","36","0","-2","26","-16","2","0","18","-2","0","0","4","0","36","8","4","4","18","24","6","6","24","24","0","24","-24","-1","33","-4","-12","2","22","0","-4","11","-24","2","24","1","16","28","2","-10","-42","4","0","-9","-10","-24","-24","6","6","36","0","-8","0","0","-16","-8","-28","0","-8","12","26","4","2","1"],"lmfdb":"agrees","curve":{"cremona":"30a1","lmfdb":"30.a","ainvs":[1,0,1,1,2],"rank":0,"torsion":6},"derived":{"al":[[2,1],[3,-1],[5,1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.107,"computed":"atlas","estimate":{"seconds":0.209,"low":0.128,"high":0.362,"bytes":1815398},"url":"https://sagebrush.space/atlas/mf/30.2.a"}