{"label":"86.2.a","level":86,"weight":2,"dims":{"new":4,"cusp":10,"eisenstein":3,"modsym":23},"old":[[43,3,2]],"T":[[3,1],[5,3]],"status":"proven","checks":["dim M^+ at levels [1, 2, 43, 86]: [0, 1, 4, 13] (certified at ell = 2147483647)","T = [(3, 1), (5, 3)]; h of degree 4 = 1 x 4 (phi(ord eps) x dim S_k^new); 1 primes, 0 rejected"],"newforms":[{"label":"86.2.a.a","letter":"a","dim":2,"charpoly":["-5","-8","1"],"traces":["2","-2","-1","2","3","1","4","-2","5","-3","0","-1","4","-4","-12","2","-9","-5","1","3","-2","0","-9","1","5","-4","-10","4","3","12","1","-2","0","9","6","5","1","-1","-2","-3","3","2","2","0","18","9","-9","-1","-6","-5","15","4","6","10","0","-4","-32","-3","12","-12","4","-1","10","2","6","0","-20","-9","-6","-6","0","-5","28","-1","-34","1","0","2","-5","3","-10","-3","-6","-2","-24","-2","9","0","6","-18","8","-9","31","9","33","1","-11","6","0","5","18","-15","-11","-4","-24","-6","12","-10","-8","0","31","4","-6","32","-3","3","10","-12","-18","12","-22","-4","30","1","24","-10","7","-2","-1","-6","-3","0","2","20","-15","9","-6","6","16","6","-27","0","0","5","-6","-28","3","1","15","34","4","-1","-33","0","-30","-2","1","5","18","-3","-18","10","7","3","0","6","-12","2","-18","24","34","2","18","-9","10","0","-6","-6","15","18","-2","-8","-2","9","-30","-31","0","-9","-20","-33","-30","-1","-35","11","-24","-6","24","0","-14","-5","10","-18","6","15","-27","11","-12","4","0","24","-11","6","42","-12","3","10","2","8","-14","0","-18","-31","28","-4","44","6","-21","-32","-20","3","0","-3","30","-10","18","12","34","18","-15","-12","22","22","14","4","-9","-30","2","-1","24","-24","-6","10","0","-7","75","2","48","1","2","6","-3","3","-24","0","-12","-2","18","-20","36","15","43","-9","-4","6","0","-6","-11","-16","-29","-6","-9","27","34","0","-69","0","6","-5","17","6","-26","28","-6","-3","18","-1","0","-15","-18","-34","4","-4","-30","1","6","33","-14","0","-26","30","-24","2","-14","-1","36","-5","-12","-18","0","3","-6","18","-36","-10","10","-7","4","-3","-18","0","4","-6","-29","12","-30","-2","25","18","-60","-24","0","-34","-40","-2","33","-18","-27","9","55","-10","-20","0","-24","6","-42","6","30","-15","33","-18","57","2","11","8","42","2","1","-9","-24","30","12","31","-41","0","-33","9","6","20","-26","33","-35","30","24","1","0","35","5","-11","0","24","30","6","33","-24","-39","0","46","14","-64","5","15","-10","2","18","6","-6","0","-15","46","27","66","-11","24","12","-30","-4","-8","0","0","-24","-23","11","9","-6","-54","-42","8","12","0","-3","-9","-10","-8","-2","3","-8","27","14","7","0","-15","18","-30","31","-12","-28","45","4","-12","-44","0","-6","-2","21","12","32","16","20","45","-3","-18","0","22","3","57","-30","-3","10","-40","-18","-32","-12","0","-34","97","-18","-6","15","-33","12","2","-22","-12","-22","15","-14","-17","-4","28","9","9","30","-3","-2","0","1","0","-24","-35","24","-36","6","24","-10","48","0","9","7","-18","-75","56","-2","-5","-48","15","-1","0","-2","-72","-6","-66","3","-35","-3","-68","24","27","0","5","12","30","2","6","-18","18","20","-60","-36","0","-15","-8","-43","64","9","-12","4","4","-6","10","0","-30","6","-10","11","57","16","24","29","4","6","0","9","-24","-27","54","-34","-20","0","0","69","13","0","36","-6","9","5","-2","-17","-14","-6","-12","26","0","-28","36","6","0","3","-94","-18","30","1","-6","0","-48","15","-56","18","9","34","10","-4","-50","4","-33","30","-20","-1","18","-6","-18","-33","-50","14","45","0","15","26","40","-30","45","24","12","-2","32","14","0","1","27","-36","64","5","37","12","42","18","-12","0","-42","-3","-24","6","-44","-18","-12","36","-66","10","0","-10","62","7","-39","-4","-36","3","70","18","72","0","-20","-4","30","6","66","29","-24","-12","-14","30","0","2","-62","-25","-25","-18","51","60","-22","24","0","0","60","34","-72","40","10","2","12","-33","16","18","0","27","24","-9","18","-55","-36","10","12","20","-94","0","-9","24","36","-6","-20","42","-44","-6","-36","-30","0","15","-66","-33","93","18","-22","-57","52","-2","-24","-11","10","-8","-19","-42","-9","-2","-5","-1","36","9","0","24","25","-30","-64","-12","30","-31","-30","41","-36","0","24","33","-56","-9","-18","-6","6","-20","37","26","0","-33","-18","35","-16","-30","-123","-24","24","-1","25","0","-24","-35","15","-5","-92","11","62","0","-93","-24","0","-30","-15","-6","33","-33","-20","24","-30","39","-12","0","8","-46","6","-14","54","64","9","-5","-6","-15","0","10","-6","-2","-18","-18","39","-6","67","6","10","0","-21","15","1","-46","20","-27","36","-66","4","11","0","-24","12","-12","43","30","100","4","27","8","24","0","-5","0","66","24","-43","23","-69","-11","-27","-9","-44","6","46","54","-36","42","-14","-8","135","-12","21","0","-47","3","60","9","42","10","90","8","-103","2","0","-3","-40","8","4","-27","48","-14","34","-7","66","0","-15","15","-20","-18","-72","30","-12","-31","14","12","0","28","90","-45","75","-4","-12","12","33","44","-6","0","-2","6","-66","2","76","-21","66","-12","66","-32","0","-16","-24","-20","-6","-45","43","3","-56","18","0","0","-92","-22","4","-3","-12","-57","-3","30","96","3","0","-10","-26","40","70","18","-30","32","-45","12","-30","0","-60","34","56","-97","-120","18","24","6","-66","-15","0","33","-12","-12","33","-2","30","22","-21","12","-53","22","165","-15","-66","14","32","17","-68","4","-51","-28","0","-9","-20","-9","-30","-30","-6","3","-54","2","-9","0","100","-1","-128","0","42","24","-17","35","-5","-24"],"lmfdb":"agrees","derived":{"al":[[2,1],[43,-1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"86.2.a.b","letter":"b","dim":2,"charpoly":["11","8","1"],"traces":["2","2","1","2","-3","1","0","2","-3","-3","-4","1","0","0","-4","2","-1","-3","11","-3","-10","-4","3","1","-3","0","-2","0","-7","-4","13","2","8","-1","10","-3","-5","11","10","-3","-5","-10","-2","-4","2","3","3","1","26","-3","-3","0","-10","-2","-4","0","8","-7","16","-4","4","13","-10","2","-10","8","4","-1","-6","10","-16","-3","4","-5","6","11","-40","10","-1","-3","-2","-5","-10","-10","4","-2","-11","-4","2","2","-40","3","9","3","-19","1","-11","26","16","-3","2","-3","17","0","20","-10","-4","-2","4","-4","-5","0","10","8","3","-7","10","16","10","-4","26","4","-10","13","12","-10","-13","2","-1","-10","11","8","-10","4","13","-1","-18","-6","-12","10","19","-16","40","-3","18","4","13","-5","29","6","0","11","-1","-40","-22","10","-25","-1","-10","-3","30","-2","-27","-5","-12","-10","12","-10","14","4","-14","-2","-18","-11","-30","-4","-2","2","5","2","-30","-40","-18","3","10","9","-8","3","40","-19","-2","1","-19","-11","-20","26","-16","16","18","-3","2","2","30","-3","15","17","-12","0","-12","20","19","-10","2","-4","3","-2","-10","4","22","-4","-10","-5","-36","0","12","10","17","8","20","3","0","-7","42","10","-22","16","2","10","-3","-4","6","26","-10","4","-39","-10","10","13","-20","12","-6","-10","-36","-13","7","2","32","-1","10","-10","3","11","-16","8","20","-10","-14","4","-20","13","31","-1","-20","-18","36","-6","11","-12","-17","10","23","19","22","-16","-27","40","30","-3","-31","18","-18","4","-22","13","-14","-5","-36","29","-30","6","0","0","26","11","14","-1","26","-40","6","-22","40","10","-46","-25","0","-1","8","-10","-16","-3","-2","30","-8","-2","30","-27","32","-5","-70","-12","-12","-10","5","12","-6","-10","9","14","20","4","-16","-14","0","-2","9","-18","-9","-11","13","-30","-40","-4","8","-2","14","2","10","5","53","2","25","-30","-27","-40","-26","-18","-19","3","0","10","20","9","-31","-8","11","3","-30","40","22","-19","11","-2","4","1","40","-19","3","-11","-8","-20","6","26","33","-16","-1","16","18","18","-60","-3","-25","2","10","2","18","30","0","-3","22","15","-14","17","40","-12","30","0","4","-12","-16","20","15","19","13","-10","-6","2","80","-4","0","3","3","-2","-24","-10","29","4","9","22","19","-4","-39","-10","-38","-5","12","-36","17","0","-20","12","-20","10","30","17","60","8","-36","20","11","3","-10","0","-22","-7","-31","42","27","10","0","-22","-40","16","4","2","-9","10","10","-3","-53","-4","-10","6","0","26","29","-10","27","4","-36","-39","43","-10","11","10","-4","13","-40","-20","-21","12","-4","-6","-8","-10","-28","-36","7","-13","-10","7","-80","2","-21","32","-23","-1","64","10","-4","-10","-2","3","-21","11","0","-16","-9","8","-19","20","-34","-10","-30","-14","6","4","-20","-20","-52","13","32","31","0","-1","-36","-20","-8","-18","-26","36","-46","-6","-10","11","15","-12","44","-17","0","10","-4","23","44","19","-30","22","60","-16","24","-27","-53","40","-36","30","-27","-3","-30","-31","18","18","60","-18","0","4","0","-22","24","13","74","-14","-18","-5","18","-36","-20","29","4","-30","-27","6","62","0","-6","0","1","26","-48","11","50","14","70","-1","54","26","25","-40","63","6","-48","-22","27","40","60","10","-8","-46","44","-25","5","0","28","-1","-3","8","2","-10","0","-16","34","-3","4","-2","8","30","4","-8","26","-2","-72","30","-70","-27","7","32","-44","-5","14","-70","-8","-12","12","-12","-10","-10","70","5","12","12","-18","-6","-88","-10","18","9","-27","14","-27","20","50","4","16","-16","32","-14","32","0","10","-2","-20","9","0","-18","80","-9","8","-11","10","13","16","-30","-24","-40","-30","-4","-41","8","-100","-2","-12","14","4","2","12","10","-40","5","6","53","41","2","10","25","48","-30","-12","-27","22","-40","21","-26","1","-18","-31","-19","-52","3","-8","0","15","10","60","20","2","9","-46","-31","0","-8","0","11","-12","3","22","-30","-30","40","31","22","12","-19","10","11","-120","-2","-1","4","-40","1","-39","40","16","-19","-43","3","-12","-11","30","-8","-35","-20","72","6","37","26","65","33","8","-16","-18","-1","-60","16","-80","18","30","18","-54","-60","-19","-3","-18","-25","72","2","-30","10","-30","2","-33","18","17","30","18","0","63","-3","-11","22","60","15","-32","-14","-12","17","-12","40","-12","-12","-47","30","-12","0","-13","4","-8","-12","-23","-16","-50","20","-11","15","-31","19","-21","13","160","-10","-14","-6","0","2","62","80","11","-4","-75","0","51","3","40","3","-22","-2","22","-24","-13","-10","12","29","0","4","4","9","-20","22","-58","19","34","-4","49","-39","-28","-10","-12","-38","-44","-5","-70","12","-56","-36","34","17","15","0","0","-20","-53","12","10","-20","10","10","30","30","44","17","22","60","66","8","-40","-36","32","20","-110","11","47","3","-12","-10","40","0","0","-22","-28","-7","68","-31","143","42","40","27","12","10","14","0","-18","-22","-54","-40","15","16","-70","4","-16","2","80","-9","24","10","64","10","38","-3","-28","-53","20","-4","25","-10","6","6","1","0","79","26","-19","29","14","-10","-40","27","0","4","13","-36","-64","-39","24","43","42","-10","34","11","-50","10","-3","-4","-56","13","-16","-40","-22","-20","-67","-21","15","12"],"lmfdb":"agrees","derived":{"al":[[2,-1],[43,1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.092,"computed":"atlas","estimate":{"seconds":0.211,"low":0.128,"high":0.364,"bytes":1839145},"url":"https://sagebrush.space/atlas/mf/86.2.a"}