{"label":"233.2.a","level":233,"weight":2,"dims":{"new":19,"cusp":19,"eisenstein":1,"modsym":39},"old":[],"T":[[2,1],[3,1]],"status":"proven","checks":["dim M^+ at levels [1, 233]: [0, 20] (certified at ell = 2147482481)","T = [(2, 1), (3, 1)]; h of degree 19 = 1 x 19 (phi(ord eps) x dim S_k^new); 2 primes, 0 rejected"],"newforms":[{"label":"233.2.a.a","letter":"a","dim":1,"charpoly":["1","1"],"traces":["1","1","-2","-1","2","-2","4","-3","1","2","6","2","6","4","-4","-1","-6","1","-4","-2","-8","6","0","6","-1","6","4","-4","-2","-4","4","5","-12","-6","8","-1","-6","-4","-12","-6","2","-8","-2","-6","2","0","2","2","9","-1","12","-6","-6","4","12","-12","8","-2","-10","4","-6","4","4","7","12","-12","10","6","0","8","-8","-3","-14","-6","2","4","24","-12","2","-2","-11","2","2","8","-12","-2","4","-18","10","2","24","0","-8","2","-8","-10","10","9","6","1","-6","12","18","-18","-16","-6","-4","-4","-14","12","12","-4","-10","8","0","2","6","-10","-24","12","25","-6","-4","-4","-12","4","2","-3","4","12","-12","12","-16","10","8","18","-6","0","18","-8","-4","-8","36","-1","-4","-14","-18","6","-14","2","-10","12","-6","24","8","12","2","2","12","10","0","-11","2","-2","-24","2","-12","24","23","-12","-4","2","18","4","-4","-6","20","10","-22","-2","-2","24","12","0","-12","-8","-36","-2","16","-8","-6","-14","10","10","-24","-9","-6","6","-14","3","-20","-6","-8","-12","4","18","0","-6","-24","-16","-10","6","16","-4","-4","-12","16","-14","28","-12","-36","12","22","20","-1","-10","14","-8","-6","0","-48","6","1","6","4","10","-4","-24","14","4","30","25","10","6","18","-4","-24","-12","-4","-12","0","-4","0","2","24","-17","26","4","-24","-12","-2","-12","-4","36","-12","-16","-20","-10","-10","8","8","6","-48","-6","-6","0","-14","18","4","-24","-6","-4","16","8","16","36","8","5","19","-4","-20","14","14","-18","-20","18","24","-14","0","-2","-8","-10","12","4","-12","-6","-4","-24","-36","8","-22","36","26","2","8","-2","18","12","-12","14","8","0","24","11","-6","2","28","-6","8","-24","4","-2","-6","-12","20","8","22","23","20","12","24","-4","8","6","0","18","-2","-4","2","-4","24","30","18","20","-16","-10","48","-22","-8","-6","-3","-2","-50","-24","-28","12","18","0","2","-12","-24","8","-6","-36","24","-6","-12","16","14","8","-4","-6","26","6","48","10","-2","-10","10","-24","0","-27","24","-6","4","-6","-22","-14","32","1","-30","-20","24","6","-22","-8","-36","-36","-14","4","12","-18","-40","0","4","30","-36","-24","18","16","-22","-10","2","18","6","16","-24","4","-72","-4","-6","-4","-26","16","8","14","0","28","18","-36","9","-36","-20","-12","20","22","28","28","18","-1","12","10","20","14","48","-24","10","-6","-24","0","42","-48","6","2","-16","1","-28","-6","40","4","-4","30","-12","-4","4","24","-6","14","4","-20","-36","30","0","-25","20","10","42","18","-4","18","0","4","12","-24","12","-4","-32","-4","-8","12","24","0","-24","-12","-12","0","-46","-2","18","24","-56","-11","-16","26","36","-4","12","-24","-36","-36","-34","-2","-34","12","8","-4","-24","12","-23","-12","-10","16","12","-20","-8","-30","44","-10","54","-8","2","8","4","-30","-28","-48","-4","6","-6","-6","8","0","8","-14","24","-18","-2","4","-12","-8","72","-6","42","4","-20","16","-44","24","18","16","20","-36","12","8","0","7","-14","19","-20","4","8","-20","-36","42","12","14","16","18","-16","-20","12","6","10","24","-48","14","28","0","12","-6","-26","-8","10","10","50","12","-32","-20","16","-12","12","6","26","-4","-8","-72","-6","-36","-26","-8","0","-22","40","12","-19","26","48","-2","36","8","34","-6","20","18","4","-12","54","-12","-8","-6","-46","8","-16","0","8","24","-20","33","-60","-6","-32","-2","-18","28","-24","-2","-14","8","22","24","10","4","72","-6","-32","-6","0","12","-44","20","-36","-40","34","22","-4","-23","18","20","40","36","-28","24","-12","4","-12","8","12","2","-36","0","28","-18","24","-2","36","-12","-12","2","-2","4","2","24","24","42","-8","18","-24","-20","2","-16","2","-30","0","48","72","22","-28","-8","-18","-2","72","-3","-60","2","2","-50","-20","-72","13","-28","12","-12","-6","18","-36","0","60","2","-34","12","48","-24","46","24","-28","-6","2","36","-16","24","28","-2","0","-12","-20","-16","22","14","0","24","-34","-4","-56","6","-12","26","-60","34","42","48","-52","-10","-6","-2","-4","-30","48","10","-8","24","-48","0","-8","-9","4","24","22","6","8","4","-40","-18","-36","-22","24","14","-30","32","-12","-5","10","-30","-84","20","0","24","20","18","-6","-22","-8","8","-16","-36","4","-12","8","-14","24","-4","2","12","12","-54","12","-40","-36","0","-6","4","28","42","-54","-36","-24","24","16","18","2","48","-25","-22","12","10","46","2","100","6","-32","6","0","-16","-6","-24","-8","12","18","-72","-50","4","-16","-6","54","20","36","-26","-38","-16","12","8","60","42","10","0","-48","-28","-46","18","-28","-12","-14","9","44","36","40","-20","2","-36","8","20","-66","-22","-8","28","-44","-12","0","18","-8","1","36","12","16","30","-4","20","56","-14","-6","48","-22","-8","12","10","24","6","-48","-24","12","0","8","42","-48","48","6","6","18","-10","18","-16","-36","-1","44","-28","-72","-18","-14","40","-52","-4","38","-4","0","10","32","-12","24","4","-84","4","-36","72","-14","-6","-12","-14","24","4","-24","-28","-15","-36","-4","-30","20","0","-22","-75","-48","20","10","-10","72","42","12","6","-46","-4","60","-18","-14","0","8","12","-12","12","-16","24","0","12","54","20","-8","-32","-28","4","2","-8","-24","36"],"lmfdb":"agrees","curve":{"cremona":"233a1","lmfdb":"233.a","ainvs":[1,0,1,0,11],"rank":0,"torsion":2},"derived":{"al":[[233,-1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"233.2.a.b","letter":"b","dim":7,"charpoly":["3","0","-19","-11","27","30","10","1"],"traces":["7","-2","-8","2","-3","-2","-17","-6","7","-8","1","-9","-12","1","-6","-4","-5","-1","-8","-3","18","-3","-16","13","4","16","-23","-9","3","24","-24","16","-6","-5","6","34","-10","13","8","-4","16","25","-3","28","18","5","-8","11","16","46","16","-12","1","24","-35","29","25","8","9","20","-6","15","-25","-26","-7","15","-36","11","29","10","-9","-31","-7","-41","-33","-6","4","13","-26","2","27","-31","2","7","0","-7","-24","-7","21","-32","17","-33","26","-6","7","2","-11","7","29","-8","-1","1","-56","9","16","33","-5","-53","16","-50","10","14","-3","-90","-5","13","-27","37","-23","33","-2","9","24","-55","-12","-14","-47","-5","-28","-22","35","-81","-12","33","-2","-8","-3","47","-3","30","43","-28","-9","-27","-21","6","6","43","-4","-88","4","-8","-18","19","48","-16","-27","-6","-9","34","60","-39","15","-26","70","7","-4","-46","45","9","-7","-11","-19","-17","-14","-5","13","26","23","-43","2","-59","27","-7","11","19","-9","40","76","65","10","21","14","-39","69","5","27","-57","-55","-13","40","-54","41","9","30","0","-42","18","-25","-53","38","-29","22","-2","67","70","72","-34","-25","15","78","123","-81","-68","60","53","-13","115","29","41","5","41","-7","-17","-20","-6","90","30","56","-39","4","24","18","29","4","-7","-84","29","-15","-10","-21","-54","23","-63","26","-4","4","91","22","5","30","-53","-8","11","-10","26","-81","-42","-22","26","-10","-5","-19","98","22","5","-2","13","-61","31","-60","-119","-68","-44","-36","26","-29","8","-14","-70","79","60","3","-98","-77","-19","-68","-60","-4","-10","-11","44","-25","-14","-76","-27","-11","-86","73","72","4","-40","-93","-1","-49","5","30","-107","37","73","-13","3","-17","15","-35","81","15","6","-25","149","33","-11","26","31","12","-12","-16","-4","-2","-7","-84","148","-16","-85","-39","31","-23","-49","38","-123","84","-27","30","-127","29","41","-55","10","-48","-85","69","-75","-75","92","-7","-68","-85","87","-71","4","43","95","11","-19","92","48","-54","-73","-4","-63","17","-34","-33","-32","87","20","96","20","-35","20","-43","-57","-38","-25","-20","150","42","-20","-21","-15","-10","-56","64","79","8","-52","63","-16","39","89","37","-21","-56","-86","-33","-61","-55","18","95","-70","13","-22","-49","72","-76","151","25","22","-56","84","-72","11","-31","-61","79","17","11","-51","-65","23","-2","68","-10","-104","-13","-75","64","86","-34","154","-75","-76","-53","79","74","-6","-37","16","7","113","93","-32","-4","-47","-67","2","45","14","124","4","-2","8","-7","-95","78","10","-28","88","-36","-163","45","44","-49","13","-85","104","-17","70","-132","47","44","118","-105","-6","-84","49","84","117","43","-78","3","-40","-19","57","21","-51","86","95","25","5","12","60","-1","-50","86","-34","-21","118","38","45","-72","75","29","-73","151","71","-5","37","23","-34","-52","-28","-114","-41","63","85","-17","37","-61","-8","-2","40","33","38","66","-91","108","-93","-63","83","-25","-7","30","-37","-16","-6","17","29","-44","-46","-40","1","161","108","24","56","-42","45","41","-120","3","0","-15","95","-3","-75","17","46","21","-45","-18","63","-47","14","-121","47","-51","96","2","-66","-107","24","-113","138","60","9","93","-89","87","35","-52","20","-75","-18","50","146","-75","36","52","-99","3","-8","54","-37","-148","-49","1","4","-13","33","23","-118","-77","16","17","-15","161","-37","74","75","-41","34","-77","-63","88","84","28","104","-103","13","18","-47","-107","75","-213","-92","-37","-71","16","-108","-41","-29","-9","-96","72","6","102","76","-18","-17","-72","-63","-56","-90","-76","-267","-25","-48","102","27","54","-15","-35","-3","-18","-104","-31","-69","64","19","-58","2","88","-261","-119","27","-34","91","-65","-146","-11","-73","-40","158","-15","-32","-36","114","8","10","-96","-83","-96","-151","121","-30","8","32","38","18","-104","-40","76","-14","122","58","-59","-90","-25","106","99","-171","40","5","95","22","-82","-22","-74","-54","-26","-19","-100","130","-37","14","-51","37","88","103","-13","-119","36","-50","69","-82","37","23","-36","-15","-103","-115","3","-53","68","126","10","39","31","-63","-55","135","-87","51","-56","-6","57","81","110","156","-83","-41","-83","-218","-29","17","-78","50","70","-29","-43","17","31","-25","87","200","46","124","22","89","-34","-10","66","91","69","-14","54","211","100","-101","147","-19","58","117","-72","-136","62","38","-86","-36","123","-80","-177","-138","46","-45","40","-70","157","39","-93","-172","-74","37","11","-69","54","-11","-60","-26","-70","64","146","134","-93","-101","170","22","-12","-120","-8","14","4","-22","-42","217","13","-64","163","-47","52","-28","28","-12","50","-80","-21","-96","75","90","-84","10","147","-139","74","107","119","178","-5","156","27","37","-109","19","-25","-47","132","111","20","55","-71","105","-77","-196","171","-150","90","43","137","-108","63","100","126","15","-175","18","-10","36","-28","-36","-130","-35","125","21","-24","-47","82","-33","38","116","4","-52","96","-70","244","-7","30","72","36","12","66","31","119","191","-156","-35","-62","-150","125","-261","117","-2","-68","-69","135","124","-9","-93","193","-144","58","57","-8","-33","36","-239","71","166","-61","-8","-16","17","-76","290","-67","-37","-68","-132","-20","-70","-9","79","132","77","-102","-196","-1","-25","51","1","-90","-36","83","75","82","-79","45","-37","38","-93","-44","10","-59","-20","-18","0","-146","52","144","-275","65","-45","6","1","10","-161","-104","25","-99","-40"],"lmfdb":"agrees","derived":{"al":[[233,1]],"fricke":1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"233.2.a.c","letter":"c","dim":11,"charpoly":["2978","-13020","20420","-12042","-1331","4406","-1223","-347","195","-6","-8","1"],"traces":["11","-2","10","14","-1","-2","15","-6","11","2","-5","11","4","-11","10","8","7","-21","8","-13","14","5","8","-23","16","-12","13","27","-9","-20","24","-24","-2","-1","-26","-2","14","-3","-4","2","-8","-19","15","-20","-12","-35","8","-5","4","-26","-28","4","-5","-60","5","-31","-27","-16","5","-36","-2","-9","15","-22","-31","-1","-2","-17","3","-24","3","-39","23","7","-9","-14","-34","31","36","4","19","13","6","77","-20","-7","28","33","-19","0","1","39","12","56","29","-56","33","11","-15","40","-21","45","90","33","-36","-3","-5","121","20","10","0","54","-31","32","25","1","-31","35","39","13","-50","67","-20","25","-36","-82","43","55","-20","-6","-1","-17","12","57","-2","-6","-31","-13","19","-54","-37","48","3","49","-39","-18","72","19","-4","82","16","16","-52","13","2","-88","17","4","23","24","-24","-95","23","72","-14","-31","36","-92","-27","57","-35","13","-47","-23","34","-73","-55","46","-11","-39","6","17","7","-55","-11","11","7","-14","2","-15","-12","65","-32","-27","-35","-15","-41","11","91","-25","-44","34","-35","-27","-82","-86","30","-26","-31","-29","-28","49","-44","-10","3","-140","-12","-2","-73","55","-34","-21","45","-48","-72","-67","53","-69","-27","13","-51","-83","11","151","-72","36","-2","52","-24","33","-64","12","34","-3","-36","21","72","49","-23","-58","-77","138","-45","91","52","-88","-56","31","26","-7","14","71","56","91","-26","-58","-65","8","34","78","6","-17","-37","68","-2","-15","8","-23","19","-39","26","153","-24","-36","8","-84","23","-128","-42","268","19","24","-17","-42","31","-11","-68","-42","-20","-84","-21","-34","23","34","-116","23","9","-22","101","-116","72","132","5","23","-73","-31","72","-15","17","39","9","-57","-25","231","33","-7","17","30","-39","47","-7","105","62","-57","4","120","36","-48","-16","-83","88","152","84","69","113","-109","-69","-13","-50","125","-46","-29","10","13","135","-143","13","-38","-4","69","17","53","-13","-44","-15","84","159","63","-23","-76","45","19","-9","65","-4","2","26","-255","-32","197","121","-140","67","10","-41","-80","-2","74","31","-36","-15","-73","66","83","-108","-66","88","-40","-61","-55","66","224","16","-25","54","-148","75","88","-25","-75","45","29","8","-2","-49","71","-91","-68","5","-118","37","122","65","-134","114","-39","47","-66","68","-28","28","187","29","63","-29","-79","-37","-127","9","-65","70","-128","-18","198","-25","-213","60","-114","-34","150","-67","32","47","-103","4","-14","7","56","-137","-65","-11","48","18","-31","29","-2","61","-198","-28","20","90","28","-43","-15","-110","-74","60","-86","-8","9","5","-88","-67","-135","91","-132","19","46","-84","-171","-20","2","-13","-46","-4","-87","4","17","-5","-138","47","-24","9","-195","-29","79","36","-23","-49","-71","74","72","-69","-164","-62","-122","-17","-94","-6","-17","4","-25","145","71","-21","-173","19","-95","-85","-170","-98","-188","40","179","79","-49","27","-83","-125","-72","-104","124","-17","-16","72","119","44","-105","77","69","-25","-17","80","-11","-120","8","105","1","76","80","32","-133","15","44","40","56","78","73","89","108","-89","-34","-127","123","101","161","-11","90","-111","-161","48","-181","85","84","35","7","-71","196","-74","-22","-137","-40","93","114","-40","29","141","31","-73","259","156","30","-175","80","32","-46","145","124","50","-39","-59","-128","64","227","-74","105","-31","-28","-31","59","167","-136","-53","-168","5","109","-11","-37","-40","131","-17","150","75","23","32","332","-76","48","-95","21","94","-75","13","103","101","-112","31","-311","68","-180","-97","55","-41","258","34","58","-80","98","-114","39","8","-183","-28","-64","226","-83","-37","12","122","27","-134","-107","5","-35","-86","-32","93","35","-62","-5","174","0","0","-233","-7","203","-38","47","-65","-102","13","-29","-30","-24","-83","-86","-44","-26","10","130","92","245","112","115","77","90","-164","48","-42","44","50","128","32","190","-94","-258","-99","90","63","-54","153","-23","46","149","-129","-24","186","126","50","350","-38","33","-48","-34","-125","18","-63","3","-100","301","147","-67","-92","150","17","30","-223","75","-52","-199","65","-91","-5","-49","28","382","-50","145","-41","-179","81","-45","-51","-107","-24","-94","-77","-27","-60","4","-83","-103","149","118","187","-27","26","126","-102","99","-25","-77","123","99","47","12","66","-148","18","185","-90","174","66","105","-237","166","-2","3","48","-25","-25","41","18","-227","-6","-132","-66","262","22","60","51","-64","-131","-24","-142","-49","74","-76","-175","-197","251","-56","146","-209","75","3","-102","-19","-152","194","-86","-32","58","226","-137","59","-60","32","-112","-32","152","-92","-72","-208","-14","103","-23","-98","-7","5","-140","-82","12","126","-184","40","-21","-204","-57","-10","56","104","11","-65","-54","3","-75","174","-29","164","53","-123","289","91","-109","-19","-20","-199","-138","-49","-159","-215","-53","60","-39","106","108","-231","33","0","-95","168","-56","-21","137","-10","-150","10","-232","-308","-30","-39","-147","-199","-82","-111","18","35","-94","-16","6","-148","32","-82","-100","141","2","-60","-68","184","52","-83","-165","-89","-152","13","230","82","-79","-141","-83","14","168","7","75","212","-85","83","-19","-112","-22","-195","68","-21","-4","-71","-153","-78","-43","-248","-140","61","100","-108","-147","9","8","144","-96","-6","27","-17","36","69","98","-58","-25","35","-49","-27","46","166","-83","165","-38","41","65","43","-94","-237","-12","-118","81","28","42","-110","-202","144","102","-47","91","-161","2","5","18","-141","-162","-331","-25","86"],"lmfdb":"agrees","derived":{"al":[[233,-1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.168,"computed":"atlas","estimate":{"seconds":0.233,"low":0.142,"high":0.403,"bytes":1949364},"url":"https://sagebrush.space/atlas/mf/233.2.a"}