{"label":"229.2.a","level":229,"weight":2,"dims":{"new":18,"cusp":18,"eisenstein":1,"modsym":37},"old":[],"T":[[2,1],[3,1]],"status":"proven","checks":["dim M^+ at levels [1, 229]: [0, 19] (certified at ell = 2147478649)","T = [(2, 1), (3, 1)]; h of degree 18 = 1 x 18 (phi(ord eps) x dim S_k^new); 2 primes, 0 rejected"],"newforms":[{"label":"229.2.a.a","letter":"a","dim":1,"charpoly":["0","1"],"traces":["1","-1","1","-1","-3","-1","2","3","-2","3","-3","-1","-6","-2","-3","-1","-7","2","3","3","2","3","4","3","4","6","-5","-2","-6","3","4","-5","-3","7","-6","2","2","-3","-6","-9","6","-2","7","3","6","-4","6","-1","-3","-4","-7","6","-10","5","9","6","3","6","4","3","5","-4","-4","7","18","3","-10","7","4","6","-9","-6","-2","-2","4","-3","-6","6","6","3","1","-6","11","-2","21","-7","-6","-9","-18","-6","-12","-4","4","-6","-9","-5","-5","3","6","-4","2","7","9","-18","-6","10","-16","5","-16","-9","2","-2","8","-3","-12","6","12","-4","-14","-9","-2","-5","6","-4","3","4","18","3","7","-18","-12","3","6","10","15","-21","-8","-4","-14","6","6","9","18","2","18","2","-3","-2","-9","-4","-15","9","14","6","-12","6","-10","-6","-10","15","8","-1","-14","-6","9","-11","-9","6","23","-21","-6","-7","18","6","8","3","4","18","-18","-6","15","12","5","12","-6","-4","21","-6","-10","9","20","7","-2","5","18","3","-2","-6","4","12","-10","-2","-12","7","-18","-9","-8","6","-9","6","-14","10","-9","16","-21","-15","8","16","-2","-9","42","-2","2","-10","-8","-8","22","-3","-1","12","-6","-18","19","-12","-18","-4","6","14","-8","3","-22","2","16","-5","9","-6","-18","12","11","-3","0","4","-12","-18","21","-17","-6","-7","4","-18","12","12","30","-9","30","-6","-18","10","12","-15","7","7","-12","8","-12","-4","1","14","-8","-18","-14","-6","0","9","-9","-18","12","10","32","-18","-5","2","-9","3","-12","6","15","9","-24","-4","14","15","2","-3","-15","-14","7","6","9","12","11","-18","-32","10","12","-6","20","10","18","-21","-16","-8","-21","-1","-24","14","-16","18","12","-9","18","-11","-4","9","30","-2","-31","-23","8","-21","-12","6","-20","21","-12","-18","12","6","-16","-8","30","15","-6","-4","27","18","-14","18","8","18","-10","-15","-2","12","6","-5","-9","-4","-12","6","-20","-4","-27","-21","3","18","36","10","-18","9","18","-20","36","3","18","2","-14","5","0","-18","-28","-9","-12","2","-18","-6","-31","-4","6","-4","-15","10","-24","-2","-3","12","-6","-21","-9","18","-8","-9","8","8","-33","30","-14","9","6","6","11","14","-12","-30","-28","9","10","16","18","21","-19","5","19","-8","18","16","12","2","-8","27","6","-42","-36","-2","54","-2","-9","14","14","8","-18","-8","-15","-22","36","9","17","1","35","12","2","6","5","6","-12","-19","23","-12","-20","18","-10","12","-21","-6","12","14","20","8","-14","15","-12","22","8","2","15","-16","20","15","-14","-9","7","-6","42","18","-18","-4","-18","-11","14","-3","-9","0","0","-12","-6","12","23","-18","-2","-21","-4","11","-15","6","-27","-7","-18","-4","18","54","-6","-12","44","12","8","-30","-28","3","-7","-30","-8","-6","-36","18","48","-30","-18","-12","9","-15","-2","-7","15","35","48","12","-4","8","-10","12","-18","12","12","-1","-6","14","47","8","-42","6","21","14","-24","-6","-24","0","2","-27","9","9","10","-18","20","-12","16","-14","14","-32","-2","-18","22","5","30","-6","-36","9","-27","3","12","12","-2","-2","-6","-15","42","9","4","24","24","12","-22","-14","20","15","6","-2","32","-15","-12","15","-36","-14","-46","-7","-18","-18","18","-9","32","12","-20","-11","-36","6","-29","32","-9","10","-14","-12","5","18","-14","-20","-54","10","18","-18","18","-9","-33","16","40","-8","-21","21","-16","3","-12","24","8","14","-36","16","36","-6","4","-12","-40","-9","-37","-18","42","33","-18","4","-24","9","2","-30","-15","-10","15","31","-20","-23","4","-8","-10","63","22","12","9","6","24","20","-1","-7","60","12","-20","-18","12","-12","42","-18","-42","16","19","-8","-11","-30","6","-21","-18","6","4","-4","-20","-27","-12","-54","16","14","-54","18","-8","-8","0","-6","18","10","-22","-15","-24","2","38","-36","13","-6","-49","-5","-15","9","9","-20","30","12","-14","6","-18","20","-29","12","27","27","-22","-21","-32","-3","7","-6","0","-36","45","10","9","18","-12","-27","10","-18","-32","-20","-42","-36","-24","-17","-19","-18","-6","2","-34","14","16","-15","4","0","18","-18","27","28","30","3","30","12","37","2","30","18","16","18","-30","31","30","-4","34","-6","-42","-20","36","15","6","10","-24","24","12","6","48","3","48","12","7","6","42","7","21","9","24","18","-45","8","-26","27","-12","-8","22","8","26","33","1","-42","21","14","27","9","-20","-6","-14","-18","7","-11","-14","14","-69","12","-4","10","0","28","8","9","4","-10","18","-48","14","-18","19","21","12","19","-33","25","-54","-19","32","-8","-18","-18","60","-48","10","-12","6","2","-32","8","-9","-9","50","-6","5","-42","-12","36","38","6","36","-54","-3","-2","18","9","54","6","-24","-14","-24","8","70","18","14","24","-45","15","12","-22","-4","-36","57","-3","-33","-17","-15","1","-24","-35","-33","-36","7","-2","54","6","8","-5","-18","30","-14","12","-9","-19","11","-23","-63","36","28","20","-32","18","-5","10","24","-4","30","21","24","-6","12","-12","20","-42","17","-20","-60","8","18","14","-16","-21","-15","12","32","22","6","-8","8","-6","-21","-15","13","-16","-28","-20","-24","-5","-18","14","54","-9","32","-7","54","18","6","-42","12","18","28","18","27","-20","18","18","-12","-11","-57","-14","-10","9"],"lmfdb":"agrees","curve":{"cremona":"229a1","lmfdb":"229.a","ainvs":[1,0,0,-2,-1],"rank":1,"torsion":1}},{"label":"229.2.a.b","letter":"b","dim":6,"charpoly":["-4","-15","0","35","32","10","1"],"traces":["6","-4","-6","4","-3","-1","-5","-12","4","2","-22","4","1","0","-6","4","6","-6","-19","-13","-13","23","-10","-1","3","-15","-3","9","-7","9","-3","7","23","1","-11","13","2","26","16","26","-12","39","-9","-33","7","3","-4","34","15","21","-2","12","5","20","11","12","23","21","-32","1","-6","11","25","6","-21","5","2","14","-4","-8","-32","-19","10","-14","-12","-19","8","21","-5","-18","-22","-18","-14","-64","-12","25","5","68","-4","26","0","-1","19","8","-22","-56","22","-41","-39","-14","-15","-40","0","15","61","-21","-25","-28","25","-43","15","-49","15","-14","27","-46","-33","40","-9","18","38","3","8","5","12","-57","-35","-4","8","-13","-27","-25","26","-71","9","-65","19","11","21","14","27","38","13","-10","-14","32","-26","35","0","-41","-21","22","29","18","-20","-27","5","-25","21","25","18","17","-15","23","35","-13","11","54","-9","49","-25","-96","32","40","-6","-40","0","-1","-20","-39","-14","17","-5","-6","17","-60","-51","26","3","-26","-13","11","14","25","37","38","-2","44","-2","-17","62","-16","11","53","34","67","49","7","78","-43","-8","45","78","-18","84","48","-17","-19","-31","90","-44","-69","87","45","1","-10","-47","-16","-6","64","78","33","4","-26","7","-55","71","1","-49","-59","51","-97","35","-21","-18","24","3","-19","-75","-45","-4","50","-5","2","-30","-16","4","28","-41","24","-11","-12","-11","14","-24","7","22","64","-7","-84","-62","64","-62","-10","-1","-6","-4","-5","-34","-19","-48","-129","29","-16","69","65","16","50","-24","4","-28","-72","-45","98","66","-10","50","-53","-60","39","-89","35","24","-11","-47","-5","-34","-22","-40","-33","14","-70","-13","80","-57","41","50","-44","34","6","52","-77","-5","-53","-41","-24","-40","53","-53","-11","-19","20","-35","-17","5","-23","22","73","38","-67","27","13","86","118","-44","-77","-55","-88","-7","41","3","-22","1","12","-57","40","-16","71","-109","-31","-9","50","-40","-3","-17","111","79","29","-8","-42","-17","69","-21","41","35","-122","17","40","-31","63","19","-5","43","-4","40","-67","-52","-40","-2","50","52","-22","-17","95","34","-58","-12","2","17","-29","9","19","3","24","14","-108","12","5","-2","-21","-60","-102","22","-19","59","-37","-47","-103","3","57","-16","-8","42","-43","20","-91","78","57","-85","-27","-38","-93","-71","110","38","48","6","55","64","-91","58","-21","19","126","-85","0","20","-62","-23","46","48","63","16","4","59","27","-22","4","-58","-32","18","-256","-48","14","21","95","3","68","-66","123","-27","103","80","-138","15","-32","-22","50","13","19","6","9","11","171","10","0","29","25","21","71","-109","-1","7","72","-27","7","-9","159","-36","65","-51","-63","-45","1","94","-4","-48","8","11","-4","7","33","20","9","58","-25","-53","197","-31","85","70","-41","-20","0","64","49","-1","-147","-4","5","0","-29","21","-19","4","0","19","127","-92","67","0","45","3","-12","-29","3","18","27","24","-89","56","52","-131","-97","-40","-25","53","58","-1","122","25","38","121","189","-112","-7","5","33","-73","8","60","-89","-36","46","-26","-35","16","-6","-41","93","160","-62","-19","77","-73","26","58","-115","40","-49","59","-20","-24","-130","9","-12","91","1","-44","50","60","-15","-54","-60","-19","-66","96","-32","-34","39","-118","-14","-67","16","-6","-103","19","-42","104","-4","-78","0","58","59","-88","20","-99","-107","-45","19","106","-105","-98","54","-17","75","41","-83","-121","-97","21","-50","-178","48","-120","-26","-30","102","128","-13","49","-35","-23","-11","19","-59","-47","85","-82","4","-98","44","118","82","56","104","53","-36","-143","89","5","-16","13","-64","57","-131","-17","-110","-67","8","146","-42","-141","-31","-8","-171","6","-13","33","-136","-3","36","-99","92","86","99","-76","-180","-21","-47","52","8","-37","0","-125","-51","-66","-25","32","-94","-8","-38","-66","119","120","8","2","-13","107","45","-45","-33","-14","-42","-55","-7","77","-36","-17","-127","-66","-193","-90","3","22","44","-16","22","-117","-62","-64","112","68","-56","34","193","130","-95","10","5","5","173","-56","60","-14","-15","-35","32","87","-45","-43","95","28","-56","69","-112","-67","9","-71","56","-45","146","-59","109","59","-20","107","-53","-16","-80","171","-35","-62","23","-87","171","37","-113","-5","171","-14","94","52","-6","3","13","138","-164","165","1","-28","-127","38","45","-8","13","-54","-13","-27","-24","-26","192","52","21","83","44","-32","-163","129","-4","6","38","88","102","17","-16","-24","-15","-28","0","118","-36","16","-6","69","123","60","-5","49","-154","53","124","128","10","168","71","44","41","-52","37","-116","70","-18","-240","-16","-46","37","-84","-12","130","38","57","27","13","-16","-46","27","-157","-43","-132","132","-62","-22","-94","0","-123","5","-143","88","86","-1","-163","40","73","-12","71","-40","-156","117","-37","109","-36","13","162","-4","125","96","88","-83","-78","-3","26","218","-129","-8","46","50","74","33","58","-38","-101","1","7","112","-4","135","111","34","-165","32","22","66","386","76","5","-54","82","-33","134","-68","-105","-41","-10","9","51","-49","89","-37","-155","52","15","-28","-105","-64","-237","-6","249","51","-36","-6","150","-54","16","141","-104","59","-110","62","-50","-85","-44","21","-105","-114","126","100","-248","-4","-69","8","-16","-71","-18","72","14","-27","101","22","-42","32","32","-34","-80","-128","2","86","-75","35","-119","31","-94","-15","204","-141","-196","96","-128","121","-107"],"lmfdb":"agrees"},{"label":"229.2.a.c","letter":"c","dim":11,"charpoly":["50","3270","1967","-7152","1001","3286","-1275","-297","201","-8","-8","1"],"traces":["11","5","3","11","0","0","1","15","14","-3","27","-1","-7","4","-1","7","1","-4","8","-16","-7","4","-2","-16","1","-9","0","-19","17","-32","-3","30","-4","-22","27","-1","-14","-11","18","-43","18","-39","-2","14","-29","-27","14","-43","-10","15","23","-44","-11","-39","-20","-12","-22","-29","52","-20","-23","1","-9","9","3","-4","18","-1","-22","-2","31","31","-10","6","16","10","-12","3","1","-49","7","60","37","-36","-19","56","-13","53","4","22","8","-25","-17","12","37","-7","-17","-20","55","60","23","65","-15","-23","-3","29","23","-35","-3","-6","-7","39","1","-27","-5","22","-13","46","5","-73","32","50","68","-45","-9","45","-15","9","-37","-19","55","22","-40","13","-20","-8","31","23","-7","98","1","7","-1","12","0","-22","7","-17","29","77","28","23","-59","12","36","107","-55","-37","-13","-56","10","-8","-5","37","-12","34","2","-92","-38","-48","25","93","-12","-30","-90","67","-38","-3","98","37","-61","-49","-80","-36","-93","68","-62","-40","-59","85","55","54","-54","10","-37","-29","-18","-78","-44","37","-62","30","-5","0","-16","30","3","-27","-23","55","0","-15","-63","-12","-5","-3","-25","-123","17","-119","-30","151","-35","-23","-125","58","29","-79","11","-10","-6","-9","-45","-126","-29","93","13","-3","25","-112","23","23","63","0","-77","-46","-49","-105","-44","-92","36","16","-73","-56","7","27","-22","-31","-17","-8","81","38","37","55","8","29","-30","38","-11","117","25","-43","-42","-34","95","122","-9","-87","-10","147","6","69","7","49","28","-17","-20","50","26","-18","35","2","-10","89","-38","-36","-27","86","68","131","43","14","-16","-58","18","39","9","-124","-31","33","-43","188","-33","34","13","45","70","-154","64","-45","24","7","34","-54","-15","44","2","107","-31","-94","89","65","-13","168","-5","-93","25","-16","-12","-52","11","97","8","61","58","5","37","32","-57","-143","47","157","-59","52","6","22","116","19","11","55","57","-53","-6","-31","-65","42","-18","-97","140","-94","139","123","56","-60","-2","50","-47","82","57","48","-3","-27","11","-5","82","-151","2","-57","14","120","18","-33","51","21","84","-52","31","-86","-111","53","20","-35","15","-28","45","28","-50","4","3","-99","-4","-55","22","-49","26","-155","53","-78","17","57","-27","-44","-54","77","-24","68","-16","-133","89","-138","75","-176","142","-74","90","-58","-28","9","-24","-258","-14","105","-13","140","45","-40","-105","-82","1","-108","28","73","85","-106","-53","-160","-19","5","65","118","-42","-62","-31","-40","73","54","-30","-170","22","-47","-111","109","-57","-76","-21","-108","8","36","-17","-18","14","-113","-13","-43","79","-10","39","10","67","6","122","9","-67","-106","-109","-75","-45","-140","-8","-246","76","55","-157","31","-26","-196","-145","-20","-1","-95","-133","-112","157","39","39","-36","165","-41","-133","-21","-26","23","18","-14","18","21","-97","-20","47","9","52","121","29","-105","34","92","-35","-121","13","44","16","-104","50","-3","53","219","-70","33","-92","279","-40","76","11","-8","6","-177","10","28","-103","84","70","64","127","213","18","-29","-39","46","78","29","82","-113","98","-126","-180","83","-10","-86","73","95","64","-99","-41","-9","-41","-79","67","-84","12","-27","9","28","20","-249","101","143","-33","167","72","244","2","-53","-4","151","-91","256","48","-43","26","12","158","42","17","-1","-180","-157","-65","83","-8","32","10","23","30","83","187","68","-96","1","71","-45","39","-61","42","154","25","-155","-69","-65","-35","52","-78","274","-54","44","11","-135","-118","11","106","131","-35","1","25","-95","-93","129","53","-101","110","-145","-33","32","-38","45","36","10","81","153","-55","221","-70","42","22","-1","-139","94","-53","-2","93","49","68","26","24","255","-114","61","3","188","79","36","-59","-200","53","-64","128","-39","-68","-52","102","-195","47","-38","-179","107","-89","-101","-86","-161","4","-5","-164","124","48","-51","6","182","-42","-15","33","157","75","89","152","-219","-17","91","-119","-86","-40","211","-63","58","13","90","7","-218","-22","74","-65","-136","136","96","123","12","-131","76","24","96","-14","-70","-108","91","82","56","-21","41","-60","174","-221","128","-15","-127","-92","74","67","56","-199","-28","88","38","-255","-174","-61","253","77","-153","101","-53","108","-16","6","65","-102","28","-97","67","6","105","159","69","6","184","30","-19","-119","13","28","-162","-65","231","26","188","66","-389","14","79","-158","-75","83","115","62","28","-57","-25","-23","243","-99","24","-59","-130","-25","70","-64","-49","157","80","66","-229","32","195","-81","-52","159","-56","-76","36","-114","55","31","120","-76","-25","-38","-96","-47","-287","-118","169","222","-81","158","143","164","-72","-74","-296","-207","-54","19","31","-314","-124","-86","-190","22","-147","-249","-5","47","-126","-152","-162","110","-110","10","-39","199","145","-61","-259","29","25","-123","75","28","-61","-98","132","-71","-219","54","252","-57","137","-124","-47","-164","-178","73","-76","-33","112","-44","-33","-31","-115","-18","34","-49","94","-45","-288","224","-12","-3","11","5","72","-111","233","-129","122","14","-92","-48","-90","-188","152","-79","46","-137","4","270","-183","-142","-105","-85","273","-7","-319","-57","37","-112","177","20","154","-42","-55","67","-148","72","-86","-19","-28","23","-26","-179","-16","70","-187","-110","204","-13","63","90","64","4","32","-173","180","117","208","145","68","-18","107","-187","271","-16","-95","84","93","12","-10","72","-60","-62","-255","41","89","-78","-80","131","-14","-3","-223","107","156","-113","-432"],"lmfdb":"agrees"}],"seconds":0.252,"computed":"atlas","estimate":{"seconds":0.231,"low":0.141,"high":0.399,"bytes":1941591}}