{"label":"39.2.a","level":39,"weight":2,"dims":{"new":3,"cusp":3,"eisenstein":3,"modsym":9},"old":[],"T":[[2,1],[5,1]],"status":"proven","checks":["dim M^+ at levels [1, 3, 13, 39]: [0, 1, 1, 6] (certified at ell = 2147483629)","T = [(2, 1), (5, 1)]; h of degree 3 = 1 x 3 (phi(ord eps) x dim S_k^new); 1 primes, 0 rejected"],"newforms":[{"label":"39.2.a.a","letter":"a","dim":1,"charpoly":["-3","1"],"traces":["1","1","-1","-1","2","-1","-4","-3","1","2","4","1","1","-4","-2","-1","2","1","0","-2","4","4","0","3","-1","1","-1","4","-10","-2","4","5","-4","2","-8","-1","-2","0","-1","-6","6","4","-12","-4","2","0","0","1","9","-1","-2","-1","6","-1","8","12","0","-10","12","2","-2","4","-4","7","2","-4","-8","-2","0","-8","0","-3","2","-2","1","0","-16","-1","8","-2","1","6","4","-4","4","-12","10","-12","-2","2","-4","0","-4","0","0","-5","10","9","4","1","-18","-2","0","-3","8","6","12","1","-2","8","2","4","-6","0","0","10","1","12","-8","6","5","-2","-6","-4","-12","-4","-16","-3","12","2","4","4","0","-8","-2","-6","6","0","12","8","0","0","4","-1","-20","2","-9","2","-6","1","4","0","2","-16","8","1","-18","8","-6","10","0","1","8","-6","-8","4","-8","-12","1","4","0","12","6","10","4","-4","-12","-2","4","-2","-10","-4","2","0","-4","-4","8","0","4","0","8","-7","18","10","-2","-9","18","4","8","3","8","-18","40","2","12","0","0","-1","0","8","-20","-6","0","12","-24","3","-16","-2","-2","-8","2","2","4","-20","-1","-6","-20","0","-10","0","16","30","-14","1","0","-12","-8","-8","-24","2","10","5","-1","2","18","-6","0","-12","-4","-12","-12","4","0","-16","-4","-17","26","12","8","-2","-10","4","24","12","12","0","2","8","22","-2","-12","-2","4","6","-4","0","-10","12","4","24","-10","0","12","0","0","4","-24","5","-13","-20","-10","-2","-6","-9","24","6","-4","-6","0","-1","48","4","18","0","-4","2","-16","16","0","8","0","3","-6","-18","-8","-8","26","-6","-40","14","-12","0","0","-1","-1","8","2","-18","0","-8","-16","-4","-2","-8","-16","-4","18","1","6","-4","16","0","-8","36","0","6","-12","-10","-26","4","-1","20","-2","-12","0","2","8","4","24","-6","-19","-10","-5","4","4","2","16","0","6","-4","-24","4","-26","8","12","0","-10","4","-24","0","16","8","-16","3","-32","18","-12","-10","22","-2","0","-27","-4","18","16","-4","38","8","0","1","22","8","4","18","2","40","-8","6","34","12","-6","0","-48","0","8","5","-12","0","4","-8","-10","-20","0","-18","-2","0","8","-12","-4","-24","0","1","34","-16","20","2","0","-2","32","-24","9","2","-4","-2","-4","4","6","-28","22","-1","24","6","-4","-20","-8","0","2","-10","-2","0","-38","16","4","10","-8","-14","12","-1","32","0","18","-36","-48","-8","0","8","6","-24","-24","-10","-2","10","0","-5","20","-1","12","6","-8","18","-12","6","-20","0","8","-4","0","-4","-24","12","8","-12","-8","12","-36","0","-1","16","10","-4","-8","-11","0","26","0","-12","0","8","-6","-6","18","-10","44","-4","-4","24","8","4","-23","12","12","0","6","2","24","24","-4","22","36","2","30","-12","10","10","-4","4","4","-6","-2","-4","0","0","-32","-10","4","-12","18","4","-12","8","-8","-10","-12","0","-12","12","-4","0","34","0","-4","-4","-8","-24","0","7","-46","-13","-18","20","-16","-10","24","-6","2","-6","28","9","0","24","-18","2","-26","-4","-16","6","-8","0","-40","-3","-38","48","-8","-4","10","18","-16","0","-40","-4","0","-2","-2","-16","-12","48","22","0","24","-8","0","0","8","1","-19","-6","0","18","-4","-8","20","-24","20","26","-32","6","9","-40","0","-6","2","-12","-40","0","24","0","-8","-3","48","-1","16","-8","6","2","8","-6","2","0","28","8","30","-16","-2","-12","0","-2","0","8","-4","-16","-8","20","-14","18","1","-1","22","6","-40","-12","20","16","-12","0","12","-8","10","12","6","0","-24","-6","-16","-12","24","-30","12","-26","14","-4","-34","-1","0","28","0","-2","72","12","-26","0","8","6","0","8","8","-4","24","24","-24","-2","0","-19","-10","10","10","-5","8","12","1","4","-24","-2","30","16","-18","0","-32","6","32","4","0","-24","48","12","-12","-26","4","-8","-48","12","8","0","12","-10","8","-4","22","-24","0","0","-10","16","8","-8","4","-16","12","17","-30","-32","-26","-18","10","-12","-4","-30","-8","22","0","2","0","0","10","-9","-36","-4","-32","-18","-24","16","24","-12","-2","38","-12","-8","46","0","0","-5","-2","22","8","-8","0","4","-22","54","-30","2","8","-40","12","-8","16","2","0","34","-4","-12","-22","-6","0","0","4","-48","4","0","-34","8","10","7","18","-12","-16","0","-4","4","48","-24","71","-10","10","20","2","0","-20","-6","-12","-2","0","0","30","8","0","-36","-46","-4","-44","24","24","0","16","-5","12","34","13","16","32","20","-8","6","10","0","48","2","-10","32","6","-8","58","9","-44","-2","-24","-4","-48","-6","64","-4","4","-4","0","6","8","12","0","22","-40","1","12","24","-48","18","-20","-4","12","20","-18","-8","-40","0","16","2","4","10","-16","-2","-48","0","16","-38","0","-16","2","4","0","-50","30","-8","0","14","0","12","16","-3","26","32","6","0","-14","18","0","-12","8","-48","-60","8","2","0","-26","24","-30","6","16","24","40","-24","-24","-14","-15","-2","12","-10","36","0","-52","-15","0","20","-60","1","-48","12","1","2","-42","-8","-8","-18","-2","-12","16","18","36","-20","0","0","0","8","16","20","16","0","16","4","-26","-24","2","36"],"lmfdb":"agrees","curve":{"cremona":"39a1","lmfdb":"39.a","ainvs":[1,1,0,-4,-5],"rank":0,"torsion":4}},{"label":"39.2.a.b","letter":"b","dim":2,"charpoly":["-1","2","1"],"traces":["2","-2","2","2","0","-2","0","-6","2","-8","-4","2","-2","8","0","6","4","-2","0","16","0","4","-8","-6","6","2","2","-16","4","-8","-8","6","-4","12","-16","2","-4","-8","-2","-8","16","8","8","-4","0","8","-12","6","2","-6","4","-2","-4","-2","0","8","0","-4","4","16","4","16","0","-14","0","4","8","-28","-8","16","4","-6","12","-12","6","16","0","2","0","0","2","-24","-4","-16","-32","-24","4","12","24","-8","0","-8","-8","-4","16","6","-4","-2","-4","6","4","12","16","6","-16","4","0","2","-12","16","-4","0","12","-8","0","4","-2","12","32","-8","-14","28","16","-24","0","8","0","10","8","8","-16","-4","-16","0","0","4","-16","8","8","-16","-12","-4","4","6","0","-28","2","28","-24","-6","-24","-8","4","-16","-16","-2","-20","-32","-4","-8","0","-2","32","32","0","20","4","8","2","16","0","40","-12","-4","0","-12","4","-16","-24","16","28","-8","4","24","32","16","-8","20","0","-16","-16","-14","-12","20","0","2","-16","4","32","-18","8","12","0","-28","16","-32","-8","-6","0","16","-24","-4","4","-32","32","-6","16","44","12","-32","-4","-12","-8","8","6","-44","-12","16","20","32","0","-12","-20","2","32","-28","0","-16","4","0","12","14","2","-60","0","-24","0","32","-4","16","0","-16","16","16","-32","-26","-20","-24","-32","-16","4","16","24","12","0","16","24","-8","36","-8","-16","12","0","8","-12","-8","-4","-40","-8","48","48","-4","24","4","16","-4","-16","6","38","-16","-4","44","-24","-2","-32","-4","-4","32","8","6","-32","48","4","0","-64","12","-40","32","16","48","24","6","12","20","-16","64","0","4","-8","-16","0","-32","-32","2","-6","-24","-12","-56","-32","16","24","-36","-4","-20","-16","0","-4","-2","12","0","16","-8","0","-40","0","-4","-40","4","-4","24","-2","-12","-16","12","0","8","32","-8","36","-8","-22","-28","-14","16","32","28","-48","-24","16","-16","0","-24","20","-24","0","20","-4","8","-16","16","0","48","28","10","32","44","8","-36","-20","8","-16","-6","-16","40","64","-4","28","-16","-16","18","24","0","8","-28","0","16","8","4","-36","-80","-16","48","32","8","-32","-6","8","16","-16","-16","52","24","-12","12","12","-4","64","64","4","-64","28","6","-20","-48","0","-76","0","-28","0","16","2","-12","16","28","-16","-16","-24","16","-24","-6","-32","76","-24","-20","16","-8","-4","-52","4","-64","16","-16","-32","12","-16","68","-16","-2","16","16","-20","4","-16","-32","0","0","-4","-4","28","-8","4","-28","0","-14","-32","-2","24","20","32","-8","16","32","8","8","0","-24","0","20","24","-32","4","0","8","8","-32","-16","2","-32","-16","16","-32","54","0","36","32","40","24","16","-12","8","28","-4","-8","-16","0","-24","16","-12","-14","16","4","-16","-16","-16","64","-16","-24","-36","-4","16","20","-40","28","28","-64","-8","24","0","4","12","0","24","-64","4","32","72","24","16","-8","-48","-8","-56","8","20","64","24","0","-12","-52","-16","8","4","-16","80","-24","-14","4","26","-12","32","32","20","8","-52","0","64","12","2","-16","16","-16","-12","-24","4","-32","-40","32","-8","-24","-18","44","64","8","-72","0","12","16","-8","0","48","12","-28","-84","32","16","-16","-64","-32","8","-80","-8","-88","16","-6","-62","-12","0","-20","-72","16","24","-32","-24","24","-32","-4","-2","8","4","88","4","-32","40","64","32","16","0","-6","-8","6","16","16","-28","44","0","48","12","-16","-72","-32","-36","16","-4","28","0","-12","-16","36","-8","-16","-8","8","-12","36","6","2","76","-44","32","80","-12","-32","28","16","16","-48","20","24","4","32","-40","20","0","72","64","-12","0","20","-20","-48","44","2","32","28","32","-56","32","-28","36","-16","0","-64","32","-16","0","40","4","12","8","0","-32","22","12","28","12","14","-32","-8","2","-80","-48","-60","-28","48","0","-24","-16","-24","-8","0","0","-16","4","32","-16","-20","-4","56","-64","16","32","-36","0","4","-48","-16","36","40","16","-48","48","16","64","-80","-32","20","-4","-26","84","-32","-20","-76","40","-24","-24","28","-32","-28","16","-16","-8","-48","4","6","0","16","-8","-64","24","-64","-64","12","-4","20","0","0","60","16","-88","18","24","16","-24","-8","64","-16","36","4","60","-8","-32","-32","-16","24","-16","12","32","-12","0","144","-8","8","64","-64","-12","-16","-52","-8","-12","48","-4","14","4","-40","32","-32","-8","80","-4","48","-50","-20","48","-24","0","-4","0","-12","24","36","16","4","-4","-48","16","-32","-20","-4","-24","96","-16","-44","-68","6","32","-12","38","80","0","-16","-8","68","-4","32","32","44","28","48","-24","0","28","-2","-24","28","-32","-112","-16","-4","32","-80","-4","40","32","32","64","-88","8","-32","-16","6","-8","48","-32","-68","0","48","8","52","4","-16","-80","0","8","-12","-64","84","0","12","-16","32","-40","-24","-4","32","-12","8","16","12","-16","48","0","-116","24","16","64","6","-20","16","12","-64","40","20","-64","12","-16","48","-76","64","-12","-24","0","-80","92","4","-64","4","-8","4","-16","-16","-14","12","0","44","-64","-32","8","42","-32","48","-8","2","-64","-80","-6","12","56","-24","-48","16","-12","48","28","-56","-48","24","-32","-16","-32","16","32","-16","24","16","-32","-36","12","16","-4","16"],"lmfdb":"agrees"}],"seconds":0.088,"computed":"atlas","estimate":{"seconds":0.203,"low":0.124,"high":0.351,"bytes":1825190}}