# Stored data for newform 63.6.a.f, downloaded from the LMFDB on 19 April 2024. {"label": "63.6.a.f", "space_label": "63.6.a", "level": 63, "weight": 6, "hecke_orbit": 6, "hecke_orbit_code": 22517998237515839, "dim": 2, "is_polredabs": true, "nf_label": "2.2.57.1", "trace_hash": 432397663266557296, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [6, 9, 1]]], "qexp_display": "q+(-4-\\beta )q^{2}+(-2+9\\beta )q^{4}+(14+\\cdots)q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2268, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 10.10418064821778, "hecke_ring_index": 1, "level_radical": 21, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [63, 1, [29, 10], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 7], "conrey_indexes": [1], "field_disc": 57, "field_disc_factorization": [[3, 1], [19, 1]], "field_poly": [-14, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.953", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.429", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "63.404", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [7, -1]], "trace_display": [-9, 0, 18, 98], "traces": [0, 2, -9, 0, 5, 18, 0, 98, 9, 0, 204, -396, 0, -350, -441, 0, 113, -1800, 0, -3266, -2520, 0, -1752, -2088, 0, -3238, -2016, 0, 245, -6696, 0, -20, 6129, 0, 5934, 882, 0, 6232, 15210, 0, 3216, 6048, 0, -3020, 30816, 0, 25584, -11700, 0, 4802, 19701, 0, 31444, -9468, 0, -38904, 441, 0, 37314, 43938, 0, -64754, -15300, 0, -70783, -39060, 0, 24784, 14994, 0, 9996, -97416, 0, 17452, -43434, 0, -12782, -19404, 0, 51256, 70272, 0, -58338, -117558, 0, -37860, 150048, 0, -40656, -84276, 0, -17150, -150912, 0, 159468, -24264, 0, 20776, -21609, 0, -54265, 155826, 0, 50452, -41076, 0, 36678, 130968, 0, -197312, 86832, 0, 5537, -94392, 0, 143088, -81378, 0, -256146, -88200, 0, 194522, 428364, 0, 138460, -34092, 0, -202016, 166257, 0, 93576, 523170, 0, -160034, -56124, 0, -31926, -384444, 0, 383698, -123480, 0, 318672, 514584, 0, 11556, 71262, 0, 154090, -28548, 0, 80560, -9054, 0, -85848, -154080, 0, 433714, -655416, 0, -340704, -102312, 0, -920876, 295218, 0, 977886, -192780, 0, -228870, -105624, 0, -1235672, -41562, 0, -158662, -881136, 0, -253686, -120600, 0, -226814, -98784, 0, 168672, -97812, 0, 624984, -990612, 0, -351600, 508968, 0, -257456, -344862, 0, 12005, 96876, 0, -315860, 41859, 0, 80652, -328104, 0, -256788, 71532, 0, -892388, 583056, 0, 1085536, 29682, 0, 34908, 1337400, 0, -980, 792486, 0, 696864, 587916, 0, 1559656, 300321, 0, 1107054, 914850, 0, -89030, -795744, 0, 48870, -651492, 0, 962880, 635670, 0, 290766, 425736, 0, 1028728, 524115, 0, -1394624, 43218, 0, 506912, -169380, 0, -1152456, 3245886, 0, -1593888, 679248, 0, 1577633, -1517652, 0, 305368, 642096, 0, -1690842, -238536, 0, -144492, 745290, 0, -436676, -3804858, 0, -100832, -628038, 0, 263730, 5004, 0, 149356, -3044538, 0, 157584, -689364, 0, -1792370, 833760, 0, -986160, 296352, 0, -1055098, -941544, 0, -1304534, -1632582, 0, -188808, -141246, 0, 1083102, -1674288, 0, -147980, -436392, 0, -59870, 786924, 0, 948094, 1509984, 0, 552000, 495648, 0, -2474336, 363456, 0, 3951016, -5985828, 0, 435240, -198432, 0, 1253616, 2900412, 0, -79730, 4300920, 0, -315126, -573300, 0, -1229996, -4333770, 0, -513828, 777096, 0, -2278496, 2286765, 0, 2389296, 1912320, 0, 235298, 1487448, 0, -408792, 732924, 0, 2652538, 965349, 0, 3695184, -6012756, 0, -2073744, 5485662, 0, -1493340, -2843136, 0, 390414, -1941912, 0, 1540756, 1655028, 0, -1581320, 3815712, 0, 1189704, -463932, 0, -5955836, 797040, 0, 1122348, 266868, 0, 4206220, 4086432, 0, -3729720, 7536204, 0, -1906296, 5673978, 0, 2314270, -4629384, 0, 648912, 21609, 0, -2825154, -3786336, 0, 6330586, -1955196, 0, 1063643, 53856, 0, 1942640, -6647256, 0, 1828386, 674424, 0, -7599080, 1737288, 0, -2560964, 2152962, 0, 3430728, 3915324, 0, 3045696, 137214, 0, 4551292, -6450588, 0, -107814, 2524320, 0, -3172946, -5290956, 0, -5220528, 3858984, 0, 3844960, -749700, 0, 365482, 3701088, 0, 5448544, -1145664, 0, 965328, -2075040, 0, -7087764, -5165496, 0, -3468367, 4354668, 0, 2661624, -6376590, 0, -3763482, -1913940, 0, -2303936, -7714512, 0, 1724352, 4736718, 0, -3023408, 1366902, 0, -427638, 2599146, 0, 1214416, -5038848, 0, -444954, -16322832, 0, 5379994, 734706, 0, -2227032, -162828, 0, 848540, -11410110, 0, -12108871, -2326716, 0, -1979288, 1215288, 0, 489804, 2471472, 0, 5480568, 3493224, 0, -3740900, -4773384, 0, -4649888, 11667600, 0, -15002694, 6793416, 0, 9221124, 7656768, 0, 1563376, 13348710, 0, 855148, -11727279, 0, 6589122, 3439728, 0, -10928832, -2128266, 0, -1079904, 4209120, 0, 11471638, -4662882, 0, -1532400, 1187640, 0, -1498030, -752328, 0, -626318, 2862972, 0, 7421352, 720972, 0, 16388328, -950796, 0, 12650500, 13011984, 0, -2507526, -2729988, 0, -1367348, 12235302, 0, 4683288, 11063844, 0, 2511544, -16948566, 0, 12820318, 2943468, 0, -16665208, 3443328, 0, 13118634, 14039766, 0, 5973372, 4290498, 0, -1755072, 12875616, 0, -7861892, -10678752, 0, -2858562, 6294312, 0, -7613276, 8646741, 0, 8034768, -5760342, 0, 2609736, 1726290, 0, -5833548, -10052154, 0, -244360, 6584976, 0, -3387662, -2532204, 0, -1855140, -8663094, 0, 8450400, -25584192, 0, 7207060, 7352352, 0, 866248, 15745338, 0, -7973312, -10721214, 0, -11535864, -11411568, 0, -6567368, -14525910, 0, -1992144, -19271088, 0, 7313230, 887040, 0, -17700216, -4129524, 0, -3246778, 27650034, 0, -19752236, -4439160, 0, -19683128, -4441752, 0, 26559798, -4116384, 0, -840350, 8451216, 0, 2103648, -14011344, 0, -19660886, -7394688, 0, -9976476, -35446860, 0, -1455024, 5274864, 0, -3714992, 14862384, 0, 11342760, -7220934, 0, 7813932, -14474268, 0, 405238, -6402528, 0, 4408614, -1188936, 0, 11070000, 11950092, 0, 533424, -4163112, 0, -127844, 622170, 0, -11883825, 21811374, 0, 1018024, -3206304, 0, -5522880, -7171056, 0, -18122676, -1058841, 0, 32988664, 2403828, 0, 4749454, 5258484, 0, 2151840, -9725688, 0, -3077928, -865368, 0, -2658985, 25698816, 0, -10453876, 8576208, 0, 30643842, 7635474, 0, -5159096, -5627232, 0, -7341450, -8720640, 0, 17925936, 18022860, 0, 15295272, 9061812, 0, 2472148, -3432321, 0, 26096140, 12133584, 0, 37430932, -2012724, 0, -3612552, -7652808, 0, 22163326, 14505192, 0, -28883808, -11777328, 0, -49191404, -6990480, 0, 1797222, -304560, 0, 9289428, 35741826, 0, -30922752, 6417432, 0, -16916072, 25295724, 0, 9564912, -13680, 0, 36789064, -7716888, 0, -5177856, 22785480, 0, -9668288, 14226696, 0, -36506532, -327600, 0, 847168, 4254768, 0, -41282474, -19655910, 0, -2737820, -2671578, 0, 38242650, -10436580, 0, 34131168, -15228000, 0, 271313, 27055116, 0, -27721658, 21745098, 0, 20519616, -4625208, 0, -5926396, -42894216, 0, 29599444, -1745226, 0, 2411832, -17048421, 0, -11217018, -22030200, 0, 7011312, -6012720, 0, 9301776, -905328, 0, -506282, -3987522, 0, -10999632, -6718104, 0, 7387904, 39739338, 0, -5877648, 10641636, 0, -12190160, 3511260, 0, -12551154, 10450296, 0, -19861442, -28150416, 0, 6860476, -4321800, 0, -15548400, -49567392, 0, 738738, 20934396, 0, -16794226, 7356618, 0, 16804924, 10508670, 0, 9531578, -1975446, 0, -12469686, -15247728, 0, 25446106, 20989836, 0, 7456260, -24626232, 0, 1370050, -3836448, 0, 5328552, -64189512, 0, -6332268, -446166, 0, 6784540, 42522048, 0, -11318104, -1937502, 0, -43625472, -1670508, 0, 42409096, -46807272, 0, -23639424, -3371004, 0, 27843736, -31028760, 0, 32154324, 15026652, 0, -9898784, 14189256, 0, -12777464, 21028824, 0, -21445800, 8146593, 0, -55745406, -3811320, 0, 8971728, -16501968, 0, 7080426, -31667076, 0, 20355976, -892962, 0, 4585224, -14257296, 0, -32384016, -11883150, 0, 72813748, 25635330, 0, 25914352, -1026432, 0, -19386864, 32130000, 0, -12859808, -7337376, 0, -30495690, -14379480, 0, -7841666, 28605438, 0, -28982946, 41719536, 0, -59048948, -2750076, 0, 8760192, -13418910, 0, -23991408, -11714778, 0, 51770400, 47229012, 0, -21928396, -33417810, 0, -1564374, -11536452, 0, -9812928, 3865320, 0, -18129372, -18837756, 0, -48947502, -12314736, 0, 63599326, 42837156, 0, 4317688, 16269453, 0, 11168472, -46968750, 0, 18801202, 40649184, 0, 29625352, 48558996, 0, 95169720, -6050520, 0, 38898612, 32074524, 0, -23020236, -23874588, 0, -50701672, 80661024, 0, 53189392, 21315420, 0, 15614928, -36608400, 0, 91341622, 28256292, 0, -14517984], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "7.6.a.b", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [-4, -1], [0, 0], [-2, 9], [14, -10], [0, 0], [49, 0], [10, -11], [0, 0], [84, 36], [-260, 124], [0, 0], [-238, 126], [-196, -49], [0, 0], [178, -243], [-938, 76], [0, 0], [-1624, -18], [-1288, 56], [0, 0], [-696, -360], [-760, -568], [0, 0], [-1529, -180], [-812, -392], [0, 0], [-98, 441], [-3222, -252], [0, 0], [-280, 540], [2370, 1389], [0, 0], [2688, 558], [686, -490], [0, 0], [2846, 540], [6748, 1714], [0, 0], [1680, -144], [2478, 1092], [0, 0], [884, -4788], [16144, -1472], [0, 0], [10992, 3600], [-3976, -3748], [0, 0], [2401, 0], [8636, 2429], [0, 0], [16352, -1260], [-4838, 208], [0, 0], [-21000, 3096], [490, -539], [0, 0], [16416, 4482], [20944, 2050], [0, 0], [-29974, -4806], [-6440, -2420], [0, 0], [-34622, -1539], [-20972, 2884], [0, 0], [13364, -1944], [11452, -7910], [0, 0], [4116, 1764], [-50808, 4200], [0, 0], [11354, -5256], [-18944, -5546], [0, 0], [980, -14742], [-12740, 6076], [0, 0], [18176, 14904], [36512, -2752], [0, 0], [-25200, -7938], [-50904, -15750], [0, 0], [-23772, 9684], [63496, 23056], [0, 0], [-21696, 2736], [-53242, 22208], [0, 0], [-11662, 6174], [-70048, -10816], [0, 0], [68376, 22716], [-20216, 16168], [0, 0], [5978, 8820], [-9604, -2401], [0, 0], [-19622, -15021]]}