{"label":"89.2.a","level":89,"weight":2,"dims":{"new":7,"cusp":7,"eisenstein":1,"modsym":15},"old":[],"T":[[2,1],[3,1]],"status":"proven","checks":["dim M^+ at levels [1, 89]: [0, 8] (certified at ell = 2147482921)","T = [(2, 1), (3, 1)]; h of degree 7 = 1 x 7 (phi(ord eps) x dim S_k^new); 1 primes, 0 rejected"],"newforms":[{"label":"89.2.a.a","letter":"a","dim":1,"charpoly":["2","1"],"traces":["1","-1","-1","-1","-1","1","-4","3","-2","1","-2","1","2","4","1","-1","3","2","-5","1","4","2","7","-3","-4","-2","5","4","0","-1","-9","-5","2","-3","4","2","-2","5","-2","-3","0","-4","-7","2","2","-7","-12","1","9","4","-3","-2","-3","-5","2","-12","5","0","4","-1","6","9","8","7","-2","-2","12","-3","-7","-4","-10","-6","7","2","4","5","8","2","-6","1","1","0","12","-4","-3","7","0","-6","-1","-2","-8","-7","9","12","5","5","9","-9","4","4","0","3","-9","6","-4","3","-10","-5","-19","-2","2","4","2","-5","-7","0","-4","-4","-12","3","-7","-6","0","9","9","-8","3","3","7","2","16","-2","20","-12","-5","9","-22","7","-8","-4","12","10","-4","2","0","-7","-9","2","4","-4","-8","-15","-6","-8","9","2","-2","6","3","5","-28","-1","25","0","-2","-12","-12","12","-9","3","10","7","-1","0","16","2","-4","1","14","-2","22","8","-6","21","2","-9","-6","12","-20","-5","15","-7","-14","-9","2","-9","8","-4","2","-12","-12","0","0","3","0","9","-14","-2","10","4","-12","3","10","10","7","15","36","19","-7","-2","6","-2","-16","20","8","-2","24","-5","-28","7","-8","0","-26","4","12","-4","6","12","5","-1","10","7","-16","-6","-9","0","-10","-27","-12","-9","-12","-8","-14","-3","3","-17","21","-7","8","2","0","-16","-16","6","3","-20","1","-12","-13","5","-2","-3","8","22","8","7","-29","8","18","12","-30","-12","10","10","-5","4","0","10","-8","0","-9","-7","-18","9","-4","-6","-10","-4","14","-4","28","8","0","5","-6","6","-2","-8","9","-9","28","-6","20","2","-8","6","17","-3","0","-7","10","28","-15","-1","-8","-25","19","0","48","2","10","-12","4","12","-12","-4","8","9","-2","3","18","-10","-8","-21","7","1","-2","0","-8","-16","10","10","14","4","10","1","12","-14","0","6","6","-22","7","8","-7","6","-8","-7","0","-2","12","-9","-37","6","-9","-36","0","20","17","-5","-3","-15","13","-3","-8","14","14","-9","12","-2","21","27","-16","-8","6","-4","4","-2","-20","4","-18","12","-18","0","-1","0","4","-9","-18","0","22","9","-16","14","-12","-10","8","-10","15","4","0","12","24","-9","-12","-10","-24","10","4","-7","27","-5","0","-36","0","19","-35","7","-11","6","-18","-6","-14","-2","1","16","-4","-28","-9","-8","0","-2","8","-24","8","15","-2","28","15","7","-30","8","-20","0","-9","26","22","4","-48","-12","2","12","14","-6","20","12","6","-5","-26","-5","-4","-10","28","7","-9","16","20","18","-25","9","-25","0","0","10","-4","9","40","12","-28","-9","12","12","-16","24","0","14","9","-3","3","-3","-28","11","-25","-21","9","-7","24","-8","1","-6","40","0","28","-16","-16","16","-27","-2","26","-3","-8","-20","0","-1","10","36","-14","13","-18","5","-18","2","-22","-15","19","-8","12","22","-12","-8","0","-21","24","29","-2","8","32","-18","-14","-4","6","30","5","-12","-2","-10","-4","-30","14","5","25","4","-15","0","-28","-14","28","8","14","0","-48","9","6","21","4","18","-30","9","45","4","-8","2","-24","10","12","-4","-2","-14","-1","12","19","-28","-24","8","7","0","-10","25","0","6","-24","6","-11","2","0","24","12","-9","-28","-9","35","-28","4","2","11","-20","-10","2","-6","8","-40","-18","12","-17","-3","-3","18","0","20","-3","25","-10","-8","28","-7","15","48","3","-8","8","-36","-25","8","-19","-16","0","-14","-48","-24","2","34","-10","-6","36","-20","-4","0","12","16","12","-12","-20","-19","-8","-20","9","18","2","-36","-9","-24","-18","9","-10","22","8","28","7","-6","-7","18","1","-16","2","8","0","0","8","26","-16","13","-10","10","-14","-12","-14","0","4","50","-10","12","-3","-63","-12","4","-14","-5","0","-9","-2","36","-6","-10","-22","0","-7","13","-24","13","7","-21","6","1","8","9","-35","-24","0","-33","-2","10","-12","39","27","-4","37","-24","6","40","9","10","12","12","0","8","20","11","-17","14","15","-25","3","76","-15","6","-13","8","17","5","8","-21","14","-24","-14","36","27","-8","-12","0","-2","20","-21","0","-9","2","16","-31","-8","16","-6","-8","12","12","-4","-3","-2","-18","20","-36","20","2","18","-14","12","28","18","13","0","-9","1","0","0","2","-4","-25","3","35","18","16","0","30","-22","8","-27","-8","16","17","14","20","12","29","14","27","-8","12","-10","-45","-15","-51","-12","-29","0","30","12","9","-24","28","3","-10","12","-14","-10","-8","24","-10","-30","4","-4","20","-7","0","-27","43","-25","1","0","8","-36","12","0","24","-57","-18","35","-36","7","-36","11","18","-2","-42","18","-37","-6","4","14","-45","6","-12","-1","-2","16","60","4","-14","-12","-14","9","0","-8","-9","0","-28","6","-22","-8","2","-24","0","-8","0","-5","-24","2","6","28","-64","-15","-25","-21","2","30","-20","8","8","20","18","0","7","9","-45","26","-28","-22","6","-12","57","48","-20","-12","-28","-2","0","-4","20","-14","-8","-6","14","-20","-17","-36","-12","-6","-15","-5","0","26","88","7","50","4","20","-10","14","-28","-19","-21","15","9","-24","16","32","-20","8","-6","-9","25","2","9","38","25","40","0","-8","0","-48","10","-49","4","-25","45","-10","-40","-2","12","10","28","-10","27"],"lmfdb":"agrees","curve":{"cremona":"89a1","lmfdb":"89.a","ainvs":[1,1,1,-1,0],"rank":1,"torsion":1}},{"label":"89.2.a.b","letter":"b","dim":1,"charpoly":["-3","1"],"traces":["1","1","2","-1","-2","2","2","-3","1","-2","-4","-2","2","2","-4","-1","6","1","-2","2","4","-4","2","-6","-1","2","-4","-2","-6","-4","6","5","-8","6","-4","-1","10","-2","4","6","-6","4","2","4","-2","2","12","-2","-3","-1","12","-2","-6","-4","8","-6","-4","-6","-10","4","-6","6","2","7","-4","-8","12","-6","4","-4","4","-3","10","10","-2","2","-8","4","-12","2","-11","-6","-6","-4","-12","2","-12","12","1","-2","4","-2","12","12","4","10","-18","-3","-4","1","-6","12","-6","-6","-8","-6","-8","4","2","8","20","-2","-14","-4","-4","6","2","-10","12","12","5","-6","-12","-6","12","2","6","-3","4","-4","8","8","-4","12","8","-18","10","4","4","4","24","4","-8","-1","12","10","-6","-10","2","-2","22","6","6","-8","-12","-4","-14","-12","-12","-10","4","-11","22","6","16","-6","0","-12","-9","-12","-2","-2","22","-12","-2","4","-20","1","4","2","-14","4","-12","-6","-20","12","-24","-12","-8","4","6","14","-14","-18","-8","3","10","-4","20","3","24","-6","-12","-12","12","-6","2","-2","8","-8","18","6","8","-8","-4","12","12","2","20","-8","12","20","-16","10","-1","-14","0","4","2","-4","-16","18","26","2","-24","10","-24","12","10","4","-14","5","-10","6","6","-12","-4","-18","-12","12","-12","-2","-8","6","-24","-17","18","4","20","4","-6","8","16","24","12","-4","2","-12","-14","8","-8","-6","8","10","4","-4","-2","4","6","12","-6","24","4","-4","8","-8","-12","5","19","12","-36","-10","-6","-6","20","-30","16","2","4","2","4","22","-12","2","12","6","-32","8","-12","-12","-16","-12","2","-14","-4","12","-2","-12","24","-14","-16","4","-12","11","-2","22","4","18","24","16","28","6","10","0","-24","-4","2","-9","-28","12","-24","-2","-20","-6","-8","22","-16","12","-14","-2","-8","-20","34","-20","-8","-1","24","4","18","6","-15","-14","10","-4","-20","-12","16","-2","-6","-20","-12","-12","14","-24","24","-36","-12","-8","-22","-4","12","6","14","-6","16","-14","2","18","-30","-8","12","9","16","10","24","4","-14","20","-8","1","-18","24","12","6","22","-12","-40","-36","30","12","20","6","-20","2","12","10","8","8","6","8","-30","18","12","18","-6","8","-12","8","-16","-4","18","4","-6","12","24","-2","-4","20","10","-24","-3","12","-4","-20","-2","-16","4","14","18","-1","24","14","44","0","-8","12","-38","2","-24","4","18","-16","4","6","-24","26","-4","-2","24","-24","-28","30","-8","-24","2","-12","-6","10","-28","-20","20","-14","8","-5","36","-10","20","18","44","6","-14","12","-36","-4","8","-6","8","-12","-34","-12","0","-12","-2","-6","12","-8","-18","-6","-30","-24","20","-11","8","18","12","-4","-48","20","44","12","-22","-6","4","-8","-4","16","36","8","-19","12","-10","4","-12","2","16","-36","8","-14","12","-8","-6","-8","-28","30","-4","8","6","-10","-6","4","12","-12","-24","-2","-40","-4","34","6","4","4","-48","-6","22","-24","28","4","-22","-12","34","8","-2","8","12","-12","-2","7","-14","19","-28","-12","-12","-36","24","-30","-4","-6","24","6","-12","20","20","-10","-6","16","-24","-2","40","4","10","6","10","4","12","-22","-10","-12","-40","-10","-24","12","24","-6","10","-32","24","24","-6","-12","-28","12","-8","-16","2","-4","-19","2","16","14","60","-4","-16","36","36","-2","-12","12","-6","24","4","6","2","-16","16","-4","-8","-12","42","33","40","-2","24","-22","-14","4","-16","6","10","24","24","-16","10","28","24","18","8","10","-12","0","-32","-24","24","20","14","2","4","9","18","-28","-36","36","0","-24","6","2","-20","-20","4","-2","-12","-8","0","-22","-8","-16","-8","36","-36","-14","52","2","-34","-8","-20","-28","-48","34","-12","20","-22","-8","-12","-3","12","24","16","-4","20","18","-30","2","-12","-15","-28","14","6","10","-2","-12","13","-20","12","12","34","16","12","10","-48","-6","30","20","-8","-12","-42","-36","-4","14","-6","24","-16","24","-32","-12","-24","-12","-44","8","-22","-22","-16","-12","-2","12","4","-6","-12","14","-20","-34","14","16","36","14","-6","2","-6","54","40","-30","12","8","-16","12","24","3","28","16","2","-10","32","24","-28","12","-12","-14","24","-20","30","-8","72","-5","1","-18","-40","-24","-8","12","-28","18","-6","22","0","12","-16","-40","-44","-12","-4","30","4","-12","-6","20","-40","18","8","-20","-2","-2","2","12","-4","14","-18","8","0","-8","-24","6","-18","24","7","-30","-12","-18","18","12","10","6","8","-6","20","-8","34","-12","4","24","-22","-16","-34","4","-24","18","38","-20","-44","-6","38","-12","48","24","24","-6","-18","-4","24","-20","-30","10","-12","-8","6","-3","26","-12","40","-4","-30","-60","12","-2","44","16","-24","4","-8","-6","8","18","-36","1","-36","24","8","42","28","44","-16","0","-6","-8","-12","4","24","-38","24","-2","16","-24","38","12","-64","18","8","16","-10","4","-6","-30","-46","-24","6","-26","-32","-4","48","-6","-6","24","4","24","10","-28","-12","10","16","-8","20","24","20","2","-4","-36","42","-6","-12","-10","48","-28","20","-28","5","20","-8","14","28","8","50","-15","-24","36","-12","10","8","20","-4","6","18","44","-4","-6","2","-14","32","36","-20","-36","48","4","4","8","50","30","56","8","-40","12","46","-34","-40","-36"],"lmfdb":"agrees","curve":{"cremona":"89b1","lmfdb":"89.b","ainvs":[1,1,0,4,5],"rank":0,"torsion":2}},{"label":"89.2.a.c","letter":"c","dim":5,"charpoly":["-2","10","-6","-8","4","1"],"traces":["5","-1","-3","11","-1","-3","8","3","2","-3","6","-15","0","-14","9","11","-13","-18","13","-31","-12","-14","1","-5","4","-4","3","12","2","5","19","15","-4","-11","4","30","-14","23","22","-11","-2","16","1","6","-26","23","-4","-45","9","16","-19","12","-11","25","6","10","-7","-14","0","57","4","-13","10","11","-12","48","4","-15","-39","-10","-2","-22","-25","-6","-24","21","-8","-50","54","-55","-7","38","-20","-40","-11","3","12","-78","5","22","-20","33","-27","-28","5","-7","13","-29","8","4","14","75","-13","4","16","3","-10","-1","-3","78","-14","44","8","-53","-31","38","16","-38","6","19","21","-4","16","43","9","-18","21","71","-9","-4","-4","-12","20","-56","7","-35","-18","47","8","-76","10","18","-8","34","-34","25","-25","-50","44","-4","52","77","22","-68","-5","54","-6","-2","33","-83","-8","7","1","14","4","-50","-8","20","-9","35","-28","9","15","-4","44","-62","-8","-1","6","-42","4","28","6","5","22","63","-2","-8","4","-77","19","-51","4","-81","-10","-61","-22","-96","-26","80","18","-98","-40","-55","-18","49","8","-24","-28","-20","-28","-45","46","70","-7","71","20","39","-15","38","-40","110","28","-2","-20","0","4","-29","20","-5","-28","-66","70","-8","0","24","-10","-4","39","111","28","51","-14","-20","79","-92","-6","-67","12","-65","8","94","20","-23","17","-5","-55","53","-20","24","48","-24","-60","140","23","8","-3","36","-29","-71","94","25","40","46","-56","-149","3","40","18","58","-34","-6","-26","34","15","4","-48","50","16","66","11","-31","6","95","-24","-94","-40","48","-46","-72","-40","-22","-8","63","28","6","6","44","45","67","-12","-50","-22","-6","-74","138","9","-9","56","-39","-14","-12","-61","-89","-48","37","-71","70","36","-140","2","-56","-16","-8","-28","-80","-52","-87","-66","27","92","30","52","-83","71","-11","-78","0","-24","12","-6","-86","-6","8","-38","11","-36","66","56","22","-10","204","-67","8","-19","2","-80","91","-20","94","-62","-105","19","-58","-21","12","60","36","45","-115","-3","-17","-3","-85","-60","-68","4","-17","36","50","51","-9","102","82","-30","68","-50","14","-4","108","-58","38","-30","14","75","-16","60","121","-42","-70","-10","-13","68","-30","16","84","-12","-12","35","128","16","-62","28","-61","16","-202","12","-86","44","83","-9","41","22","-112","24","59","1","9","27","142","-50","104","26","-6","-1","-48","-28","0","-1","68","-36","88","-52","-112","-48","-153","10","56","-35","-95","14","128","68","-42","51","74","34","-20","-12","-12","0","30","88","-134","60","50","-26","-33","10","105","-64","-80","-56","83","43","18","8","-8","55","9","49","32","-18","-6","-52","5","-8","76","24","31","-4","-24","36","-126","14","-76","103","-39","-29","-121","-8","3","59","39","-13","-35","-48","-40","35","-68","-26","-108","4","-88","-36","-8","-9","36","10","61","62","-36","48","-3","66","-132","70","13","-2","-53","-38","18","-30","-79","-65","-84","20","-74","-24","-72","-52","19","84","-83","-22","24","2","-148","-10","-48","-84","-62","13","34","-72","-42","-10","170","8","153","23","-56","29","84","28","-62","-54","-48","38","34","24","113","42","73","52","-6","-62","-5","5","-30","-32","-82","-40","16","-38","136","72","122","-31","-100","3","-48","84","68","-41","68","10","87","8","8","16","30","-23","58","0","-112","-28","-129","28","-81","-1","-64","8","-22","-33","-62","86","122","90","126","100","118","-84","79","81","133","-120","-20","20","-63","13","30","-84","104","17","-33","0","-77","-68","88","-86","-23","-44","67","80","18","-6","12","-72","-20","6","54","-70","-74","76","-16","4","4","-30","132","12","4","-59","-144","52","-47","-70","22","46","123","6","-36","31","-8","38","-8","12","-61","32","-19","-66","57","128","126","-8","76","-62","92","22","-28","61","2","-74","-106","-14","-2","152","-48","4","-170","32","3","61","120","40","74","-145","-102","-7","-58","-104","114","54","12","-112","97","7","-8","-79","-73","11","42","-71","-4","-45","23","84","60","-7","138","0","20","67","143","-48","-107","34","106","-52","75","30","20","-94","-88","36","-60","-37","79","-50","-179","-105","75","6","-53","14","71","8","79","-71","112","73","-76","144","-94","-24","-185","-20","-12","40","-66","-156","-221","-56","-9","-134","-130","-39","-70","100","-118","96","-92","-12","234","-67","-190","-90","-82","24","32","2","-82","-98","22","-120","46","-87","-34","-69","77","-20","116","-108","92","25","63","-41","-2","20","-10","74","22","8","55","48","0","-19","44","32","74","147","-52","43","-48","-20","-168","-33","117","-51","-68","3","100","122","28","29","28","-60","-153","-42","-68","62","102","70","-24","-48","22","20","-88","-24","57","72","-7","-81","57","-27","214","86","108","-12","-76","68","55","38","151","96","-39","30","-185","-2","82","-66","34","-79","-152","32","98","39","210","40","-3","70","204","-18","-64","-62","110","-88","-27","48","12","-25","40","-16","124","-4","44","-42","-88","84","8","-92","-137","-16","46","-30","4","-44","-11","97","-115","114","-102","128","-136","-24","68","-36","66","-25","-143","43","90","114","-58","-110","68","9","-72","40","-4","-48","-124","0","108","68","60","0","-114","-36","64","-59","-148","88","6","91","163","-56","130","-28","101","2","120","-136","-84","84","106","81","-81","59","185","-8","70","-12","8","-64","-44","23","-271","6","-27","26","-163","-52","-200","26","22","-4","78","67","92","-23","-49","72","164","138","72","50","-234","-46","-41"],"lmfdb":"agrees"}],"seconds":0.163,"computed":"atlas","estimate":{"seconds":0.205,"low":0.125,"high":0.355,"bytes":1854058}}