{"label":"169.2.a","level":169,"weight":2,"dims":{"new":8,"cusp":8,"eisenstein":13,"modsym":29},"old":[],"T":[[2,1],[3,1]],"status":"proven","checks":["dim M^+ at levels [1, 13, 169]: [0, 1, 15] (certified at ell = 2147483053)","T = [(2, 1), (3, 1)]; h of degree 8 = 1 x 8 (phi(ord eps) x dim S_k^new); 1 primes, 0 rejected"],"newforms":[{"label":"169.2.a.a","letter":"a","dim":2,"charpoly":["1","-4","1"],"traces":["2","0","4","2","0","0","0","0","2","-6","0","4","0","0","0","-10","6","0","0","0","0","0","12","0","-4","0","-8","0","6","-12","0","0","0","0","0","2","0","-12","0","6","0","0","-16","0","0","0","0","-20","-14","0","12","0","-6","0","0","0","0","0","0","0","2","12","0","2","0","0","0","6","24","0","0","0","0","30","-8","0","0","0","8","0","-22","18","0","0","0","0","12","0","0","-6","0","12","0","12","12","0","0","0","0","-4","6","0","20","0","0","0","12","-8","0","0","0","0","-30","-24","0","6","0","-24","0","12","-22","0","0","0","0","0","4","0","-32","0","36","0","0","-12","0","0","0","0","-8","0","0","12","0","-10","0","-6","-28","0","0","0","0","12","6","0","-12","0","-26","0","-12","18","0","0","0","0","0","48","0","0","0","-18","0","-16","-12","0","0","0","0","-24","0","0","-22","0","4","0","-30","24","0","0","0","0","36","4","0","24","0","-14","0","0","4","0","0","0","0","12","-18","0","12","0","0","0","20","-6","0","0","0","0","0","-48","0","0","0","60","0","0","-4","0","0","0","0","-36","0","0","-12","0","-12","0","16","0","0","0","0","0","-20","2","0","36","0","-12","0","42","36","0","0","0","0","38","-6","0","0","0","6","0","24","0","0","0","0","0","-12","24","0","-30","0","54","0","24","14","0","0","0","0","24","-8","0","24","0","0","0","-16","-18","0","0","0","0","24","-30","0","-66","0","-8","0","-60","12","0","0","0","0","0","40","0","60","0","20","0","0","8","0","0","0","0","24","0","0","-22","0","-72","0","-18","0","0","0","0","0","-48","12","0","46","0","-60","0","0","-12","0","0","0","0","-60","12","0","0","0","0","0","-48","-12","0","0","0","0","6","-14","0","-44","0","6","0","-44","-60","0","0","0","0","38","0","0","-12","0","0","0","12","8","0","0","0","0","-18","-16","0","18","0","36","0","72","-48","0","0","0","0","0","20","0","-24","0","6","0","0","0","0","0","0","0","20","0","0","-48","0","-16","0","36","0","0","0","0","0","-12","24","0","12","0","48","0","40","34","0","0","0","0","-12","56","0","-14","0","-24","0","24","36","0","0","0","0","0","-30","0","84","0","24","0","0","-24","0","0","0","0","-30","-24","0","-24","0","0","0","-52","24","0","0","0","0","-6","-72","0","36","0","6","0","-22","-24","0","0","0","0","42","-24","0","18","0","0","0","0","96","0","0","0","0","72","0","0","0","0","4","0","-36","0","0","0","0","0","-32","0","0","-24","0","18","0","-32","36","0","0","0","0","26","18","0","0","0","-48","0","12","0","0","0","0","0","72","-44","0","48","0","-44","0","2","0","0","0","0","0","-60","-8","0","12","0","0","0","78","0","0","0","0","0","-12","84","0","-80","0","72","0","-24","2","0","0","0","0","0","48","0","6","0","-18","0","-28","-24","0","0","0","0","0","0","0","8","0","60","0","50","0","0","0","0","0","-68","36","0","-6","0","6","0","60","-36","0","0","0","0","-12","-48","0","0","0","-22","0","0","-26","0","0","0","0","40","-18","0","-12","0","0","0","-42","-66","0","0","0","0","-36","-36","0","0","0","0","0","-60","-96","0","0","0","0","-24","0","0","-96","0","-48","0","30","36","0","0","0","0","0","38","0","16","0","-12","0","0","18","0","0","0","0","-54","0","0","80","0","-72","0","-12","0","0","0","0","0","48","-24","0","-36","0","-60","0","-24","-114","0","0","0","0","8","24","0","0","0","0","0","24","96","0","0","0","0","-22","-12","0","64","0","26","0","-48","4","0","0","0","0","0","18","0","-30","0","0","0","-24","66","0","0","0","0","84","32","0","72","0","60","0","-52","84","0","0","0","0","0","36","0","-72","0","76","0","0","-12","0","0","0","0","-24","0","0","-36","0","0","0","-24","70","0","0","0","0","48","-24","0","0","0","48","0","4","-84","0","0","0","0","-6","0","0","0","0","-24","0","66","66","0","0","0","0","72","-60","0","54","0","-18","0","108","8","0","0","0","0","12","-50","0","28","0","-42","0","48","0","0","0","0","0","-40","54","0","20","0","12","0","30","-16","0","0","0","0","0","12","0","-6","0","-28","0","0","24","0","0","0","0","-32","0","0","-36","0","48","0","-72","0","0","0","0","0","0","-54","0","-20","0","48","0","72","-60","0","0","0","0","-24","-132","0","0","0","24","0","-4","-18","0","0","0","0","-120","-56","0","6","0","0","0","0","-6","0","0","0","0","44","36","0","78","0","0","0","-48","20","0","0","0","0","-12","120","0","0","0","14","0","40","-12","0","0","0","0","0","0","0","16","0","24","0","0","12","0","0","0","0","84","0","0","-38","0","12","0","18","0","0","0","0","0","12","-20","0","-24","0","-10","0","-144","0","0","0","0","0","-36","48","0","0","0","-96","0","4","-36","0","0","0","0","34","108","0","-42"],"lmfdb":"agrees"},{"label":"169.2.a.b","letter":"b","dim":3,"charpoly":["-1","3","4","1"],"traces":["3","-2","-2","0","-4","-1","-3","-3","-3","5","-8","0","0","-5","-2","2","-2","9","-4","0","2","3","-5","9","-5","0","1","14","-1","-1","-5","7","10","13","4","-7","12","12","0","-3","-7","8","13","0","11","8","-18","1","-4","1","-1","0","1","-3","6","-4","5","3","-19","7","4","1","-4","-11","0","5","-1","-21","-6","2","-27","-4","9","-8","15","-21","8","0","-5","-5","-1","-14","-7","-7","5","-18","-18","15","-11","-12","0","0","22","5","3","-21","7","5","1","-7","5","-11","-3","0","9","-24","2","14","20","-11","-15","-9","27","-8","16","14","0","22","-19","-5","-7","-12","28","-14","15","5","-22","19","3","0","-17","-7","-17","10","8","9","20","-3","-14","-21","12","11","0","-2","20","22","5","7","12","4","-1","18","16","18","-12","0","-9","43","25","7","5","-25","40","14","3","-7","-14","-16","0","-15","11","7","-24","-2","-2","-3","22","-9","15","0","28","0","-19","-9","-9","4","3","14","13","-16","-5","-2","6","-35","0","-7","1","-24","-16","26","-25","-43","15","14","-14","-12","19","0","13","-6","6","21","11","15","-29","-22","-9","10","1","7","0","-4","-21","14","-9","-11","-5","7","-39","-13","-17","-34","-19","0","24","-28","-13","22","-48","-6","-12","21","21","35","3","21","0","40","-21","-31","0","-21","4","31","-8","-28","25","5","-5","0","22","-5","8","-31","-27","30","-9","7","-16","4","-25","8","0","-4","25","14","15","7","-16","24","-13","13","-2","21","-9","0","21","7","-17","-4","14","-63","-28","-1","16","-26","-12","-15","0","-14","-6","-18","27","9","11","-27","14","-35","-19","-6","-9","0","-38","27","-11","-63","40","23","-16","24","1","-1","33","28","0","-15","-32","35","32","5","5","49","-5","70","27","-1","-29","0","-25","28","32","-33","18","1","8","16","-27","21","-28","27","0","-35","9","-3","43","49","15","-3","-23","3","-19","21","-21","0","-19","8","26","-8","-35","20","20","-21","9","-37","4","11","0","-25","50","35","38","-48","-18","20","1","-32","-34","42","22","0","8","11","2","18","23","28","3","48","2","6","40","-9","0","49","-22","-31","-39","8","-12","7","-4","49","-9","-15","35","0","49","-32","-77","-7","-55","31","11","27","8","16","31","-35","0","31","-29","-11","-14","41","17","-28","2","-31","4","1","4","0","44","7","31","21","-15","-31","-13","-22","42","-7","-32","8","0","-5","-23","12","-17","-14","-35","-26","-6","-17","-13","15","-38","0","8","-23","-8","47","-23","-38","23","-21","-50","11","-82","14","0","-41","20","-7","-28","35","27","-46","-29","-9","55","-42","-11","0","-20","13","48","14","33","28","-28","-70","0","39","-37","-19","0","-56","-11","10","-72","-24","-27","37","25","-21","48","-34","72","0","-65","11","-59","42","-29","-52","15","2","-42","25","19","-28","0","20","-5","-41","-31","-1","13","-35","75","26","-35","-28","-8","0","34","-28","3","2","-29","-1","-58","-10","-1","-35","34","-29","0","19","12","25","-44","-7","-29","20","29","6","-47","13","-27","0","15","21","-15","46","86","-26","38","-49","56","28","23","33","0","77","42","0","37","-41","18","1","-18","8","23","21","-29","0","8","-29","21","-17","36","70","35","38","-31","-49","39","16","0","42","-43","42","0","-8","43","15","9","49","17","55","60","0","-9","2","-11","-28","-15","-9","57","12","-4","-92","6","-49","0","-8","27","-58","92","-17","49","-28","-11","-71","-16","22","60","0","-43","-21","44","-30","32","0","12","16","69","-14","-12","48","0","-56","32","43","39","-84","0","-11","-27","35","34","-25","-32","0","-80","-16","35","-26","29","2","6","56","-36","51","61","11","0","-3","66","-56","27","46","-21","18","-28","14","1","-21","-57","0","-30","20","19","-41","44","0","-30","-38","61","-38","-29","-3","0","7","53","76","4","12","52","-41","36","-63","-52","-14","-7","0","-18","-13","-25","7","-11","-71","-2","21","-23","-7","48","-21","0","3","-69","-36","-9","8","21","56","-37","16","44","-19","42","0","34","7","-43","-59","16","-31","-18","-9","-48","91","-12","-44","0","35","-35","-10","2","14","-89","46","62","0","22","-94","0","0","65","-17","51","2","26","22","-26","-56","39","-48","-34","13","0","19","-3","-35","-21","-13","-9","-63","11","13","-17","35","-30","0","6","16","-62","24","-49","-7","-37","12","-51","-3","-22","71","0","14","12","-16","-27","-53","-54","69","43","-7","68","0","-45","0","12","7","56","49","-53","63","-42","5","2","74","-17","-70","0","-40","0","3","-78","-45","-6","0","-112","-58","-10","19","75","0","-10","7","-70","80","-51","56","-24","-35","9","-21","-3","-16","0","-34","-56","-20","13","21","19","-47","-35","4","-77","-19","55","0","-6","-34","32","43","-34","-2","26","0","3","3","1","23","0","46","-87","49","-45","49","-24","-34","-21","19","-13","-35","-75","0","69","1","-7","13","23","-7","59","44","51","19","-28","70","0","35","-41","-38","10","84","52","18","17","7","34","121","-18","0","63","-31","51","-21","9","-18","-35","6","-43","41","-9","56","0","-41","34","33","27","24","-5","21","55","71","-48","-9","4","0","12","70","-50","-4","-20","-28","-15","42","-17","-91","-21","-137","0","-23","76","-25","13","14","22","-25","-68","-63","-20","40","-19","0","-45","25","-41","-98","-29","17","61","14","33","-29","25","-8"],"lmfdb":"agrees"},{"label":"169.2.a.c","letter":"c","dim":3,"charpoly":["7","-7","0","1"],"traces":["3","2","-2","0","4","1","3","3","-3","5","8","0","0","-5","2","2","-2","-9","4","0","-2","3","-5","-9","-5","0","1","-14","-1","-1","5","-7","-10","-13","4","-7","-12","12","0","-3","7","8","13","0","-11","-8","18","1","-4","-1","-1","0","1","3","6","-4","-5","-3","19","-7","4","1","4","-11","0","5","1","-21","-6","-2","27","4","-9","-8","15","21","8","0","-5","5","-1","-14","7","7","-5","18","-18","15","11","-12","0","0","-22","5","3","21","-7","-5","-1","-7","5","11","-3","0","9","24","2","14","-20","11","15","9","27","-8","-16","14","0","22","19","-5","-7","12","-28","14","-15","5","-22","-19","3","0","-17","7","-17","10","-8","-9","-20","3","-14","-21","-12","11","0","-2","-20","22","5","-7","-12","-4","1","18","16","-18","-12","0","-9","-43","25","7","-5","25","-40","-14","3","-7","14","-16","0","-15","-11","7","-24","2","2","3","-22","-9","15","0","28","0","-19","9","-9","4","-3","-14","-13","16","-5","-2","-6","-35","0","-7","-1","-24","-16","-26","25","43","-15","14","-14","12","19","0","13","6","6","21","-11","-15","29","22","-9","10","-1","7","0","-4","21","14","-9","11","5","-7","39","-13","-17","34","-19","0","24","28","-13","22","48","6","12","-21","21","35","-3","21","0","40","21","-31","0","21","-4","-31","8","-28","25","-5","-5","0","22","5","8","-31","27","-30","9","-7","-16","4","25","8","0","-4","-25","14","15","-7","16","-24","13","13","-2","-21","-9","0","21","-7","-17","-4","-14","63","28","1","16","-26","12","-15","0","-14","6","-18","27","-9","-11","27","-14","-35","-19","6","-9","0","-38","-27","-11","-63","-40","-23","16","-24","1","-1","-33","28","0","-15","32","35","32","-5","-5","-49","5","70","27","1","-29","0","-25","-28","32","-33","-18","-1","-8","-16","-27","21","28","27","0","-35","-9","-3","43","-49","-15","3","23","3","-19","-21","-21","0","-19","-8","26","-8","35","-20","-20","21","9","-37","-4","11","0","-25","-50","35","38","48","18","-20","-1","-32","-34","-42","22","0","8","-11","2","18","-23","-28","-3","-48","2","6","-40","-9","0","49","22","-31","-39","-8","12","-7","4","49","-9","15","35","0","49","32","-77","-7","55","-31","-11","-27","8","16","-31","-35","0","31","29","-11","-14","-41","-17","28","-2","-31","4","-1","4","0","44","-7","31","21","15","31","13","22","42","-7","32","8","0","-5","23","12","-17","14","35","26","6","-17","-13","-15","-38","0","8","23","-8","47","23","38","-23","21","-50","11","82","14","0","-41","-20","-7","-28","-35","-27","46","29","-9","55","42","-11","0","-20","-13","48","14","-33","-28","28","70","0","39","37","-19","0","-56","11","10","-72","24","27","-37","-25","-21","48","34","72","0","-65","-11","-59","42","29","52","-15","-2","-42","25","-19","-28","0","20","5","-41","-31","1","-13","35","-75","26","-35","28","-8","0","34","28","3","2","29","1","58","10","-1","-35","-34","-29","0","19","-12","25","-44","7","29","-20","-29","6","-47","-13","-27","0","15","-21","-15","46","-86","26","-38","49","56","28","-23","33","0","77","-42","0","37","41","-18","-1","18","8","23","-21","-29","0","8","29","21","-17","-36","-70","-35","-38","-31","-49","-39","16","0","42","43","42","0","8","-43","-15","-9","49","17","-55","60","0","-9","-2","-11","-28","15","9","-57","-12","-4","-92","-6","-49","0","-8","-27","-58","92","17","-49","28","11","-71","-16","-22","60","0","-43","21","44","-30","-32","0","-12","-16","69","-14","12","48","0","-56","-32","43","39","84","0","11","27","35","34","25","-32","0","-80","16","35","-26","-29","-2","-6","-56","-36","51","-61","11","0","-3","-66","-56","27","-46","21","-18","28","14","1","21","-57","0","-30","-20","19","-41","-44","0","30","38","61","-38","29","-3","0","7","-53","76","4","-12","-52","41","-36","-63","-52","14","-7","0","-18","13","-25","7","11","71","2","-21","-23","-7","-48","-21","0","3","69","-36","-9","-8","-21","-56","37","16","44","19","42","0","34","-7","-43","-59","-16","31","18","9","-48","91","12","-44","0","35","35","-10","2","-14","89","-46","-62","0","22","94","0","0","65","17","51","2","-26","-22","26","56","39","-48","34","13","0","19","3","-35","-21","13","9","63","-11","13","-17","-35","-30","0","6","-16","-62","24","49","7","37","-12","-51","-3","22","71","0","14","-12","-16","-27","53","54","-69","-43","-7","68","0","-45","0","12","-7","56","49","53","-63","42","-5","2","74","17","-70","0","-40","0","3","-78","45","6","0","112","-58","-10","-19","75","0","-10","-7","-70","80","51","-56","24","35","9","-21","3","-16","0","-34","56","-20","13","-21","-19","47","35","4","-77","19","55","0","-6","34","32","43","34","2","-26","0","3","3","-1","23","0","46","87","49","-45","-49","24","34","21","19","-13","35","-75","0","69","-1","-7","13","-23","7","-59","-44","51","19","28","70","0","35","41","-38","10","-84","-52","-18","-17","7","34","-121","-18","0","63","31","51","-21","-9","18","35","-6","-43","41","9","56","0","-41","-34","33","27","-24","5","-21","-55","71","-48","9","4","0","12","-70","-50","-4","20","28","15","-42","-17","-91","21","-137","0","-23","-76","-25","13","-14","-22","25","68","-63","-20","-40","-19","0","-45","-25","-41","-98","29","-17","-61","-14","33","-29","-25","-8"],"lmfdb":"agrees"}],"seconds":0.165,"computed":"atlas","estimate":{"seconds":0.216,"low":0.132,"high":0.373,"bytes":1872295}}