{"label":"194.2.a","level":194,"weight":2,"dims":{"new":9,"cusp":23,"eisenstein":3,"modsym":49},"old":[[97,7,2]],"T":[[3,1],[5,3]],"status":"proven","checks":["dim M^+ at levels [1, 2, 97, 194]: [0, 1, 8, 26] (certified at ell = 2147483137)","T = [(3, 1), (5, 3)]; h of degree 9 = 1 x 9 (phi(ord eps) x dim S_k^new); 2 primes, 0 rejected"],"newforms":[{"label":"194.2.a.a","letter":"a","dim":1,"charpoly":["-12","1"],"traces":["1","1","0","1","4","0","-4","1","-3","4","4","0","-4","-4","0","1","6","-3","-6","4","0","4","-4","0","11","-4","0","-4","0","0","0","1","0","6","-16","-3","-8","-6","0","4","-2","0","-8","4","-12","-4","0","0","9","11","0","-4","6","0","16","-4","0","0","6","0","10","0","12","1","-16","0","6","6","0","-16","0","-3","-10","-8","0","-6","-16","0","8","4","9","-2","-2","0","24","-8","0","4","14","-12","16","-4","0","0","-24","0","-1","9","-12","11","-2","0","0","-4","0","6","18","0","-10","16","0","-4","6","0","-16","0","12","6","-24","0","5","10","0","0","24","12","8","1","0","-16","6","0","24","6","0","6","-2","0","-22","-16","0","0","-16","-3","0","-10","0","-8","4","0","8","-6","-18","-16","0","0","-16","8","0","4","16","9","4","-2","0","-2","-8","0","3","24","18","-8","-20","0","-44","4","0","14","18","-12","16","16","0","-4","-32","0","24","0","0","-24","-8","0","-2","-1","0","9","-6","-12","-8","11","0","-2","0","0","-8","0","12","-4","-24","0","26","6","0","18","-32","0","0","-10","0","16","-24","0","-16","-4","-33","6","4","0","2","-16","0","0","10","12","0","6","0","-24","-8","0","-14","5","0","10","36","0","24","0","0","24","2","12","-16","8","0","1","-6","0","32","-16","0","6","24","0","24","24","0","6","-6","0","-12","6","0","-2","44","0","-32","-22","0","-16","-6","0","-28","0","0","-16","8","-3","19","0","0","-10","26","0","24","-8","0","4","16","0","32","8","0","-6","40","-18","0","-16","0","0","-16","0","-14","-16","48","8","-8","0","0","4","0","16","-36","9","-44","4","0","-2","0","0","6","-2","24","-8","24","0","2","3","0","24","0","18","-8","-8","0","-20","-18","0","-24","-44","0","4","18","0","0","14","0","18","0","-12","17","16","0","16","-40","0","0","-4","6","-32","-24","0","-28","24","0","0","0","0","28","-24","0","-8","-12","0","-64","-2","24","-1","-18","0","-24","9","0","-6","32","-12","-2","-8","0","11","14","0","0","-2","36","0","-32","0","-2","-8","0","0","-24","12","-8","-4","0","-24","24","0","-10","26","0","6","66","0","-40","18","0","-32","32","0","-2","0","0","-10","24","0","-40","16","-27","-24","6","0","56","-16","0","-4","26","-33","-8","6","0","4","64","0","-34","2","0","-16","-6","0","16","0","0","10","-16","12","-24","0","0","6","-32","0","-66","-24","-18","-8","-24","0","32","-14","0","5","-4","0","16","10","0","36","-20","0","0","24","-48","0","0","0","22","24","0","2","8","12","-8","-16","0","8","14","0","40","1","0","-6","0","0","0","32","0","-16","22","0","-2","6","0","24","0","0","-7","24","-18","24","8","0","72","6","0","-6","36","0","32","-12","0","6","-40","0","8","-2","-30","44","0","0","-32","-32","0","-22","34","0","32","-16","0","-6","42","0","24","-28","-36","0","-10","0","32","-16","0","8","-44","-3","-38","19","0","0","8","0","24","-10","48","26","-22","0","0","24","0","-8","-30","0","-96","4","0","16","-12","0","-6","32","-18","8","20","0","-32","-6","0","40","0","-18","-22","0","0","-16","-6","0","-6","0","0","-16","-56","0","41","-14","0","-16","-48","48","-16","8","0","-8","32","0","-36","0","0","4","-26","0","16","16","0","-36","0","9","24","-44","0","4","24","0","24","-2","30","0","30","0","6","6","0","-2","96","24","0","-8","0","24","40","0","14","2","0","3","34","0","4","24","0","0","-40","18","-8","-8","0","-8","-24","0","16","-20","48","-18","-88","0","-12","-24","0","-44","-30","0","48","4","0","18","8","0","-4","0","-24","14","0","0","-64","18","0","0","48","-12","0","17","0","16","0","0","40","16","-27","-40","-48","0","26","0","0","-4","24","6","-2","-32","0","-24","-40","0","16","-28","6","24","-72","0","48","0","0","0","32","0","-32","28","0","-24","38","0","40","-8","-72","-12","-24","0","-34","-64","0","-2","26","24","0","-1","0","-18","12","0","0","-24","0","9","-64","0","24","-6","0","32","-24","-12","-40","-2","0","-8","28","0","0","11","-42","14","-40","0","64","0","0","-2","34","36","-40","0","0","-32","16","0","48","-2","-48","-8","40","0","16","0","0","-24","-30","12","10","-8","0","-4","54","0","-32","-24","0","24","-56","0","-29","-10","0","26","12","0","-20","6","0","66","32","0","20","-40","72","18","38","0","54","-32","0","32","-24","0","-80","-2","0","0","32","0","-24","-10","3","24","-96","0","30","-40","0","16","-2","-27","58","-24","0","6","-4","0","-32","56","36","-16","0","0","72","-4","0","26","0","-33","36","-8","0","6","64","0","-18","4","6","64","-28","0","-8","-34","0","2","-24","0","20","-16","0","-6","0","0","-88","16","0","0","6","0","-54","10","0","-16","96","12","58","-24","0","0","-44","0","8","6","0","-32","26","0","40","-66","0","-24","54","-18","-32","-8","0","-24","8","0","-31","32","-54","-14","-8","0","16","5","0","-4","-40","0","88","16","0","10","-34","0","56","36","30","-20","-8","0","-24","0","0","24","32","-48","-20","0","0","0","-32","0","26","22","0","24"],"lmfdb":"agrees","curve":{"cremona":"194a1","lmfdb":"194.a","ainvs":[1,-1,1,-3,-1],"rank":0,"torsion":2}},{"label":"194.2.a.b","letter":"b","dim":4,"charpoly":["2116","-576","-186","4","1"],"traces":["4","-4","2","4","-2","-2","6","-4","10","2","2","2","4","-6","10","4","-8","-10","8","-2","4","-2","10","-2","14","-4","-4","6","-6","-10","8","-4","-20","8","-16","10","-2","-8","4","2","-16","-4","-10","2","-34","-10","-4","2","-6","-14","-20","4","-4","4","-12","-6","-16","6","4","10","-4","-8","16","4","-28","20","16","-8","10","16","28","-10","-6","2","2","8","2","-4","32","-2","12","16","-20","4","-4","10","40","-2","14","34","32","10","-56","4","40","-2","4","6","8","14","8","20","-12","-4","-26","4","8","-4","36","12","-28","6","-10","16","-30","-6","12","-4","12","-10","-22","4","-32","8","0","-16","18","-4","38","28","-12","-20","-16","-16","-2","8","24","-10","-4","-16","0","-28","0","10","12","6","20","-2","-26","-2","4","-8","-68","-2","-8","4","26","-32","-52","2","4","-12","-30","-16","50","20","8","-4","4","4","-32","-10","10","-40","-4","2","-40","-14","60","-34","18","-32","-48","-10","0","56","12","-4","22","-40","12","2","-42","-4","-72","-6","-20","-8","36","-14","24","-8","6","-20","-32","12","102","4","24","26","-8","-4","-8","-8","82","4","8","-36","-2","-12","40","28","-10","-6","86","10","-10","-16","8","30","-30","6","16","-12","-24","4","-4","-12","-10","10","10","22","-20","-4","-12","32","-48","-8","-12","0","28","16","0","-18","-60","4","28","-38","-42","-28","-20","12","34","20","-52","16","52","16","44","2","10","-8","60","-24","12","10","18","4","-24","16","-24","0","-22","28","144","0","-24","-10","60","-12","2","-6","-36","-20","-24","2","-46","26","-12","2","-40","-4","60","8","32","68","-10","2","-28","8","38","-4","2","-26","-90","32","-22","52","-46","-2","-20","-4","0","12","-36","30","108","16","20","-50","-64","-20","48","-8","0","4","24","-4","-66","-4","64","32","-24","10","48","-10","-52","40","46","4","52","-2","-66","40","-80","14","-8","-60","18","34","68","-18","-56","32","-78","48","12","10","16","0","-32","-56","22","-12","70","4","24","-22","-26","40","54","-12","38","-2","10","42","-86","4","-56","72","-124","6","40","20","28","8","-12","-36","-104","14","24","-24","0","8","-80","-6","26","20","-60","32","32","-12","4","-102","36","-4","52","-24","64","-26","-20","8","-8","4","-124","8","-60","8","-20","-82","32","-4","-52","-8","-146","36","-40","2","-14","12","-16","-40","-40","-28","44","10","-42","6","-34","-86","16","-10","16","10","-20","16","-24","-8","24","-30","-44","30","48","-6","152","-16","38","12","0","24","6","-4","-48","4","32","12","100","10","-24","-10","-80","-10","34","-22","-2","20","60","4","26","12","-54","-32","4","48","-62","8","68","12","16","0","-28","-28","60","-16","52","0","86","18","-44","60","44","-4","-104","-28","-60","38","-4","42","-60","28","30","20","64","-12","-18","-34","80","-20","62","52","16","-16","-16","-52","-44","-16","24","-44","-26","-2","-52","-10","34","8","84","-60","-32","24","-8","-12","-80","-10","20","-18","166","-4","-28","24","-60","-16","72","24","64","0","-54","22","68","-28","-24","-144","26","0","112","24","134","10","20","-60","60","12","-56","-2","48","6","-112","36","20","20","128","24","-20","-2","6","46","96","-26","128","12","-46","-2","-16","40","88","4","-40","-60","24","-8","86","-32","48","-68","60","10","8","-2","-26","28","-28","-8","-22","-38","22","4","-20","-2","-8","26","-100","90","12","-32","-20","22","14","-52","48","46","128","2","12","20","-46","4","-36","0","-68","-12","44","36","-112","-30","-50","-108","-24","-16","42","-20","40","50","24","64","24","20","40","-48","-16","8","62","0","44","-4","82","-24","-74","4","-112","66","6","4","-32","-64","-6","-32","-56","24","-88","-10","-56","-48","42","10","-18","52","-52","-40","0","-46","-120","-4","36","-52","48","2","-92","66","-36","-40","54","80","28","-14","-72","8","44","60","48","-18","-2","-34","8","-68","-2","18","-56","56","-48","-32","-86","78","-12","-48","-36","-12","-142","-10","-8","-16","72","0","-176","32","44","56","-2","-22","-52","12","12","-70","-52","-4","-56","-24","-48","22","-74","26","-122","-40","24","-54","56","12","60","-38","0","2","20","-10","-16","-42","44","86","-8","-4","-94","56","-64","-72","36","124","122","-6","-98","-40","-90","-20","-8","-28","8","-8","-112","12","168","36","110","104","56","-14","-24","-24","-4","24","-122","0","-36","-8","-58","80","26","6","-136","-26","-18","-20","48","60","76","-32","-124","-32","20","12","-126","-4","36","102","96","-36","-86","4","44","-52","116","24","-136","-64","10","26","-6","20","-60","-8","42","8","-34","-4","12","124","100","-8","78","60","80","-8","-64","20","-60","82","-24","-32","124","4","56","52","118","8","36","146","-32","-36","10","40","-22","-2","44","14","28","-12","-64","16","52","40","100","40","-68","28","-8","-44","44","-10","-64","42","-88","-6","48","34","-136","86","-104","-16","-26","10","58","-16","8","-10","60","20","-6","-16","-8","24","244","8","36","-24","60","30","-108","44","80","-30","124","-48","28","6","-32","-152","-88","16","-26","-38","56","-12","-98","0","-48","-24","-26","-6","32","4","-24","48","-24","-4","100","-32","-64","-12","24","-100","104","-10","78","24","64","10","116","80","76","10","36","-34","40","22","-16","2","-24","-20","0","-60","-40","-4","-32","-26","-38","-12","-28","54","30","32","60","-4","52","-48","-70","62","6","-8","8","-68","40","-12","8","-16","-130","0"],"lmfdb":"agrees"},{"label":"194.2.a.c","letter":"c","dim":4,"charpoly":["92","-24","-24","4","1"],"traces":["4","4","2","4","-2","2","2","4","10","-2","-2","2","4","2","-14","4","-8","10","0","-2","-16","-2","-10","2","-6","4","-4","2","6","-14","8","4","-12","-8","4","10","14","0","-24","-2","0","-16","10","-2","-2","-10","-28","2","14","-6","12","4","-4","-4","-12","2","16","6","-20","-14","12","8","-36","4","24","-12","16","-8","-2","4","12","10","10","14","2","0","30","-24","8","-2","44","0","-12","-16","4","10","-20","-2","-18","-2","12","-10","32","-28","0","2","-4","14","-8","-6","8","12","20","4","10","-4","0","-4","20","-12","48","2","-22","16","18","6","16","-20","-28","-14","42","12","24","8","0","-36","-22","4","-22","24","-12","-12","-24","16","-34","-8","24","-2","28","4","-16","12","-28","10","8","10","72","14","-14","2","28","0","-20","30","-40","-24","-6","8","-4","-2","-24","44","-18","0","-10","-12","-40","-16","4","4","0","10","-6","-20","4","-2","0","-18","12","-2","6","12","-56","-10","-28","32","-44","-28","-118","0","-36","2","6","-4","-4","14","12","-8","4","-6","40","8","-38","12","-16","20","-22","4","-48","10","48","-4","-44","0","-18","-4","-40","20","-2","-12","-8","48","10","2","-18","-22","6","16","-16","18","66","6","40","16","24","-20","-12","-28","-2","-14","-6","42","60","12","-56","24","0","8","12","0","28","-36","-56","-22","36","4","28","-22","-10","24","144","-12","-54","-12","12","-24","36","16","28","-34","-14","-8","-12","24","40","-2","54","28","96","4","-32","-16","-10","12","8","-28","24","10","-20","8","-2","10","4","72","-16","14","-82","-14","16","2","60","28","-4","0","72","-20","-38","30","-12","-40","26","-24","-18","-6","98","8","22","-4","22","-2","4","-24","32","44","-32","-18","52","0","20","-10","64","-12","-12","-40","-40","-16","-40","4","34","4","56","0","-92","10","48","-6","20","-20","-66","4","-76","-2","-2","0","36","-18","-8","12","-6","-2","-44","6","72","12","18","-56","-4","-10","-88","-28","32","32","22","-44","82","-28","28","-118","6","0","-106","-36","-18","2","-90","6","22","-4","40","-4","52","14","-32","12","-4","-8","-44","4","-40","-6","-8","40","-64","8","-16","-38","-46","12","-44","-16","112","20","4","-22","-36","4","-4","-48","0","10","-28","48","-152","-4","-4","-44","12","0","-44","-18","24","-4","-68","-40","-86","20","32","-2","10","-12","108","-8","-24","48","-20","10","-86","2","2","-18","-8","-22","88","6","36","16","0","-16","88","18","-20","66","-40","6","-88","40","102","16","80","24","78","-20","128","-12","-16","-28","-92","-2","-40","-14","-28","-6","2","42","2","60","-20","12","102","-56","-6","24","-36","0","102","8","-8","12","48","0","-44","28","-20","-36","-20","-56","-82","-22","116","36","32","4","80","28","-4","-22","-20","-10","40","24","-2","144","-80","-12","42","-54","-32","-12","-22","12","-56","-24","-32","36","36","16","-32","28","-6","-34","-4","-14","-18","-8","-36","-12","96","24","48","40","-24","-2","28","54","-26","28","124","96","-16","4","-24","-32","-64","-16","14","-10","-108","12","24","8","-22","-28","-56","24","-14","10","-60","-20","-84","8","56","-2","-32","10","60","4","52","72","-16","-16","28","14","90","-82","40","-14","-28","16","54","2","40","60","-136","28","-56","-4","-16","0","-182","72","-8","-20","52","-38","40","30","-38","-12","44","-40","54","26","-2","-24","-40","-18","-48","-6","12","98","12","8","-36","22","66","-4","-84","22","124","-2","44","4","110","-24","-60","32","-28","44","84","-32","-144","-18","30","52","0","0","-54","20","-56","-10","24","64","96","-12","48","-12","-28","-40","-102","-40","-132","-16","46","-40","2","4","-32","34","-2","4","16","56","54","0","-64","-92","40","10","16","48","-86","-6","142","20","-4","-20","16","-66","-32","4","-60","-76","40","-2","148","-2","76","0","22","36","20","-18","-72","-8","36","12","52","-6","38","-2","-48","-44","-2","6","-8","72","-72","12","58","18","-100","-56","60","-4","-102","-10","24","-88","-16","-28","48","32","-20","32","62","22","-124","-44","-4","82","52","-28","-16","28","-40","-118","-26","6","-34","0","0","-106","-24","-36","-84","-18","-72","2","52","-90","-32","6","-12","22","32","-4","-46","40","16","-4","-24","52","30","14","-30","-32","-74","12","-44","-4","-124","-8","168","-44","64","4","-46","-40","72","-6","-136","-8","-76","40","54","-64","-28","8","26","-16","-26","-38","20","-46","-30","12","-80","-44","124","-16","20","112","4","20","58","4","-12","-22","32","-36","54","4","4","-4","4","-48","136","0","34","10","110","-28","140","48","50","-152","110","-4","-172","-4","-16","-44","18","12","-88","0","48","-44","-12","-18","104","24","-20","-4","-28","-68","-74","-40","44","-86","-48","20","-10","32","-66","-2","-44","10","-100","-12","32","108","28","-8","52","-24","28","48","28","-20","-124","10","16","-86","0","2","92","2","120","-18","24","-8","58","-22","26","88","-72","6","-68","36","-46","16","120","0","-4","-16","124","88","-4","18","-4","-20","96","66","-20","-40","220","6","-16","-88","32","40","-46","102","64","16","-34","80","-16","24","-46","78","0","-20","156","128","-48","-12","56","-16","20","-28","-48","-92","-8","-2","-122","-40","-80","-14","84","-28","-76","-6","52","2","-112","42","-16","2","-24","60","72","-20","28","12","-8","102","-10","-56","44","-6","-30","24","-12","-36","220","0","-118","102","62","8","40","-8","-12","12","-72","48","102","0"],"lmfdb":"agrees"}],"seconds":0.088,"computed":"atlas","estimate":{"seconds":0.235,"low":0.144,"high":0.407,"bytes":1892255}}