# Stored data for newform 63.6.e.f, downloaded from the LMFDB on 23 April 2024. {"label": "63.6.e.f", "space_label": "63.6.e", "level": 63, "weight": 6, "hecke_orbit": 6, "hecke_orbit_code": 22518273115422783, "dim": 12, "is_polredabs": true, "trace_hash": 2008623114353617352, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [18380851776, 0, 1297462320, 0, 66232188, 0, 1518438, 0, 25399, 0, 187, 0, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+(30\\beta _{2}-\\beta _{5}-\\beta _{8})q^{4}+(-2\\beta _{1}+\\cdots)q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "e", "char_is_real": false, "Nk2": 2268, "analytic_conductor": 10.10418064821778, "hecke_ring_index": 3888, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [63, 3, [29, 10], [3, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [3, 7], "conrey_indexes": [37, 46], "field_disc": 45083104704844507925958728636977541184, "field_disc_factorization": [[2, 6], [3, 6], [7, 2], [269, 2], [419, 4], [9697, 4]], "field_poly": [18380851776, 0, 1297462320, 0, 66232188, 0, 1518438, 0, 25399, 0, 187, 0, 1], "hecke_ring_index_factorization": [[2, 4], [3, 5]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.028", "prec": 17}, {"__RealLiteral__": 0, "data": "10.766", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "849.438", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "114200.991", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "5.2.3.c3", "trace_display": [0, 0, 0, 142], "traces": [0, 12, 0, 0, -182, 0, 0, 142, 0, 0, 686, 0, 0, 308, 0, 0, -1898, 0, 0, 9422, 0, 0, -18292, 0, 0, -7526, 0, 0, 37074, 0, 0, 23422, 0, 0, -55608, 0, 0, -18182, 0, 0, 69258, 0, 0, -87372, 0, 0, 25332, 0, 0, 30354, 0, 0, 34272, 0, 0, -96320, 0, 0, -89782, 0, 0, -16156, 0, 0, 380580, 0, 0, 144650, 0, 0, -187262, 0, 0, -100058, 0, 0, -685440, 0, 0, 101994, 0, 0, 75712, 0, 0, 602352, 0, 0, 752310, 0, 0, -282306, 0, 0, -120456, 0, 0, -866096, 0, 0, -384492, 0, 0, 145278, 0, 0, 920796, 0, 0, 243670, 0, 0, 548832, 0, 0, 524160, 0, 0, -3332532, 0, 0, -838850, 0, 0, 1851850, 0, 0, -271724, 0, 0, 1511900, 0, 0, 138522, 0, 0, 1125012, 0, 0, -1734908, 0, 0, -1264416, 0, 0, 1650292, 0, 0, -780896, 0, 0, 277992, 0, 0, 2147794, 0, 0, 188468, 0, 0, -6335924, 0, 0, 215216, 0, 0, 1647954, 0, 0, 1840008, 0, 0, 1883660, 0, 0, 1235976, 0, 0, 171332, 0, 0, -2575132, 0, 0, -2146548, 0, 0, -30576, 0, 0, 2834408, 0, 0, 1492206, 0, 0, -4529768, 0, 0, 354424, 0, 0, 3115336, 0, 0, 2746256, 0, 0, -1466220, 0, 0, 2683616, 0, 0, 933350, 0, 0, -5411540, 0, 0, -5135830, 0, 0, -1897840, 0, 0, -1138144, 0, 0, -3534930, 0, 0, 4598916, 0, 0, -1196976, 0, 0, 7252236, 0, 0, 4510632, 0, 0, 6000960, 0, 0, -251634, 0, 0, -4873134, 0, 0, -1450608, 0, 0, -1034466, 0, 0, -6673754, 0, 0, -4368574, 0, 0, 7067256, 0, 0, 6821544, 0, 0, 3712184, 0, 0, -20134392, 0, 0, -6346066, 0, 0, 3855528, 0, 0, -701890, 0, 0, 19453784, 0, 0, 3950358, 0, 0, -1654016, 0, 0, 1251456, 0, 0, -11978076, 0, 0, 8025926, 0, 0, 5325684, 0, 0, -1711444, 0, 0, -9782730, 0, 0, 342678, 0, 0, -20537524, 0, 0, -7312256, 0, 0, 7638444, 0, 0, 8510586, 0, 0, 49143360, 0, 0, 9987666, 0, 0, -7032676, 0, 0, -7499332, 0, 0, -14640180, 0, 0, -10895288, 0, 0, -22483580, 0, 0, -10974712, 0, 0, 6882310, 0, 0, -4528272, 0, 0, -10200080, 0, 0, -344832, 0, 0, 6218804, 0, 0, 8489194, 0, 0, 49032984, 0, 0, 7796346, 0, 0, -19145784, 0, 0, 11493292, 0, 0, 6635384, 0, 0, -35258044, 0, 0, -4787846, 0, 0, -7646016, 0, 0, 254924, 0, 0, -7481222, 0, 0, 1803456, 0, 0, -8826418, 0, 0, 24802120, 0, 0, -1733886, 0, 0, 2911832, 0, 0, 11233152, 0, 0, -20088124, 0, 0, 51971988, 0, 0, 135606, 0, 0, -15668148, 0, 0, -36207416, 0, 0, 6733916, 0, 0, -10198760, 0, 0, 983416, 0, 0, -26951472, 0, 0, -5634200, 0, 0, -23110610, 0, 0, 30222416, 0, 0, 24315396, 0, 0, 14879522, 0, 0, 21639156, 0, 0, -14182660, 0, 0, 37047012, 0, 0, -11310720, 0, 0, 4324278, 0, 0, -26994324, 0, 0, -41600700, 0, 0, 25442018, 0, 0, 22402896, 0, 0, -7588798, 0, 0, 67753604, 0, 0, 21530712, 0, 0, -109880204, 0, 0, 13311398, 0, 0, 17686130, 0, 0, 5396624, 0, 0, -1574978, 0, 0, -3852296, 0, 0, -15969884, 0, 0, -92377152, 0, 0, -23657868, 0, 0, 23973866, 0, 0, -33226720, 0, 0, 18235194, 0, 0, 62524160, 0, 0, 45006976, 0, 0, 31513692, 0, 0, 641094, 0, 0, 45737076, 0, 0, 905216, 0, 0, 43015336, 0, 0, -38738866, 0, 0, -6044192, 0, 0, -83158124, 0, 0, -70339988, 0, 0, -4602416, 0, 0, -11856960, 0, 0, 16875486, 0, 0, 27056576, 0, 0, 29780030, 0, 0, -97571236, 0, 0, 22622592, 0, 0, 59885098, 0, 0, 89761268, 0, 0, 69755740, 0, 0, -20301648, 0, 0, -27809208, 0, 0, -66581900, 0, 0, -30185746, 0, 0, 24256722, 0, 0, 30788720, 0, 0, -42106132, 0, 0, -39672750, 0, 0, -6635230, 0, 0, -24100944, 0, 0, 48277954, 0, 0, -80375232, 0, 0, 77652528, 0, 0, 47504130, 0, 0, -72789874, 0, 0, 1181754, 0, 0, -27892956, 0, 0, -50248584, 0, 0, 2396604, 0, 0, 102449016, 0, 0, 18084256, 0, 0, 102669864, 0, 0, 39939746, 0, 0, 4628484, 0, 0, -16500288, 0, 0, -20384308, 0, 0, 56746868, 0, 0, 50702634, 0, 0, -88132604, 0, 0, -149514078, 0, 0, 11955888, 0, 0, 85615904, 0, 0, 5476674, 0, 0, -163332752, 0, 0, 23222688, 0, 0, -17745644, 0, 0, 24458210, 0, 0, -46101664, 0, 0, 3585748, 0, 0, 54815628, 0, 0, 5684032, 0, 0, -10335332, 0, 0, -11302726, 0, 0, 85271340, 0, 0, -27764772, 0, 0, -36526980, 0, 0, -41098274, 0, 0, 120590376, 0, 0, -67976378, 0, 0, 57218298, 0, 0, -26549208, 0, 0, 219754584, 0, 0, 2014046, 0, 0, -105713356, 0, 0, -142251672, 0, 0, -136469484, 0, 0, 50860072, 0, 0, 31901436, 0, 0, -68561052, 0, 0, -48143278, 0, 0, 61784842, 0, 0, -172183848, 0, 0, 14783280, 0, 0, 88736134, 0, 0, 113139488, 0, 0, 372090628, 0, 0, 73731684, 0, 0, 94069696, 0, 0, 10448448, 0, 0, -81698832, 0, 0, -53952168, 0, 0, -138614700, 0, 0, -77874048, 0, 0, 6349788, 0, 0, -69098330, 0, 0, -421284032, 0, 0, -98209208, 0, 0, -26848398, 0, 0, 9953622, 0, 0, 151270952, 0, 0, 60112048, 0, 0, 3095736, 0, 0, 18624748, 0, 0, -18800832, 0, 0, 140758914, 0, 0, 7724304, 0, 0, 297931452, 0, 0, -24976374, 0, 0, 35286384, 0, 0, 244164192, 0, 0, -46027096, 0, 0, -38340044, 0, 0, -34759158, 0, 0, 56743344, 0, 0, 59205572, 0, 0, -322543438, 0, 0, -176140164, 0, 0, -105050814, 0, 0, -124233590, 0, 0, 6309450, 0, 0, 173151104, 0, 0, 201650004, 0, 0, -9553992, 0, 0, -50288448, 0, 0, 3427482, 0, 0, 73137124, 0, 0, -67411764, 0, 0, 124084520, 0, 0, -42462030, 0, 0, -103265708, 0, 0, 173527444, 0, 0, -189955346, 0, 0, -4145548, 0, 0, -93856392, 0, 0, 116275684, 0, 0, 123300792, 0, 0, -150059616, 0, 0, 50415376, 0, 0, 50000846, 0, 0, -338776548, 0, 0, 542752, 0, 0, 295627360, 0, 0, -81441292, 0, 0, 111026258, 0, 0, -124997524, 0, 0, 100710666, 0, 0, -88976570, 0, 0, -52133256, 0, 0, 139013056, 0, 0, -15418670, 0, 0, -124332488, 0, 0, 90120232, 0, 0, 77795790, 0, 0, -112248480, 0, 0, -197376214, 0, 0, 73100244], "weight_parity": 1, "has_non_self_twist": 1, "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], [1, 1, 3, 2, -1, 2, 0], [1, 1, 7, 3, 1, 3, 0], [1, 1, 21, 8, -1, 6, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "63.6.e.f", "char_is_minimal": true, "conrey_index": 37, "id": null, "nf_label": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 30, 0, 0, -1, 0, 0, -1, 0, 0, 0], [0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [13, 0, 6, 0, 0, -1, 2, 0, 2, 3, 0, 0], [0, -21, 0, -21, 2, 0, 0, -2, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, -120, 0, 0, 7, -8, 0, 7, -16, 0, 0], [0, 0, 0, -24, -3, 0, 0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [41, 0, -13, 0, 0, -7, -26, 0, 0, -13, 0, 0], [0, -21, 0, 35, 4, 0, 0, -12, 0, 0, -1, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-302, 0, -302, 0, 0, 0, 14, 0, 43, -14, 0, 0], [0, 0, 0, -76, 10, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1568, 0, 1568, 0, 0, 0, 1, 0, -7, -1, 0, 0], [0, 249, 0, 249, -30, 0, 0, 30, 0, 0, 7, -7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1464, 0, -28, 0, 0, -97, -56, 0, 0, -28, 0, 0], [0, -64, 0, 0, 0, 0, 0, 22, 0, 0, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [35, 0, 1211, 0, 0, -25, -35, 0, -25, -70, 0, 0], [0, -68, 0, 0, 0, 0, 0, 64, 0, 0, -7, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2372, 0, -1520, 0, 0, 132, -54, 0, 93, -88, 0, 0], [0, -250, 0, -250, 61, 0, 0, -61, 0, 0, 8, -8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-18, 0, -3839, 0, 0, 140, 18, 0, 140, 36, 0, 0], [0, 0, 0, 689, -106, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4672, 0, 80, 0, 0, -126, 160, 0, 0, 80, 0, 0], [0, 840, 0, 168, 41, 0, 0, -67, 0, 0, 2, 18], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3060, 0, -3060, 0, 0, 0, -133, 0, -89, 133, 0, 0], [0, 0, 0, -1724, 8, 0, 0, 0, 0, 0, 0, 7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [11382, 0, 11382, 0, 0, 0, 30, 0, -483, -30, 0, 0], [0, 184, 0, 184, 104, 0, 0, -104, 0, 0, -56, 56], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-7459, 0, 189, 0, 0, -33, 378, 0, 0, 189, 0, 0], [0, -2815, 0, 0, 0, 0, 0, -122, 0, 0, -33, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-168, 0, -4128, 0, 0, -222, 168, 0, -222, 336, 0, 0], [0, 312, 0, 0, 0, 0, 0, -68, 0, 0, 56, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3674, 0, 3198, 0, 0, 237, 240, 0, -54, 493, 0, 0], [0, -1646, 0, -1646, -160, 0, 0, 160, 0, 0, -25, 25], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-110, 0, -5658, 0, 0, -168, 110, 0, -168, 220, 0, 0], [0, 0, 0, 1202, 175, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-8128, 0, -153, 0, 0, 763, -306, 0, 0, -153, 0, 0], [0, 5278, 0, 3143, -46, 0, 0, 292, 0, 0, 36, -61], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-14896, 0, -14896, 0, 0, 0, 504, 0, 203, -504, 0, 0], [0, 0, 0, -4440, -83, 0, 0, 0, 0, 0, 0, -70], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2576, 0, -2576, 0, 0, 0, -274, 0, 350, 274, 0, 0], [0, 6987, 0, 6987, -172, 0, 0, 172, 0, 0, 140, -140], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [31984, 0, -378, 0, 0, 327, -756, 0, 0, -378, 0, 0], [0, -3972, 0, 0, 0, 0, 0, 414, 0, 0, 88, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-119, 0, -23885, 0, 0, 313, 119, 0, 313, 238, 0, 0], [0, -5458, 0, 0, 0, 0, 0, -412, 0, 0, -126, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [11444, 0, 52604, 0, 0, -1422, 44, 0, -593, -788, 0, 0], [0, -3336, 0, -3336, -264, 0, 0, 264, 0, 0, 48, -48], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [259, 0, 16457, 0, 0, 119, -259, 0, 119, -518, 0, 0], [0, 0, 0, 348, 976, 0, 0, 0, 0, 0, 0, 89], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-56586, 0, 82, 0, 0, -1848, 164, 0, 0, 82, 0, 0], [0, 5306, 0, 5628, -734, 0, 0, 221, 0, 0, -184, 80], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [16761, 0, 16761, 0, 0, 0, -812, 0, -714, 812, 0, 0], [0, 0, 0, -14373, -174, 0, 0, 0, 0, 0, 0, 259], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [13552, 0, 13552, 0, 0, 0, 720, 0, 2800, -720, 0, 0], [0, 4312, 0, 4312, 567, 0, 0, -567, 0, 0, -14, 14], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [50080, 0, -98, 0, 0, 642, -196, 0, 0, -98, 0, 0], [0, -8974, 0, 0, 0, 0, 0, -1200, 0, 0, -33, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1806, 0, -126600, 0, 0, 1773, -1806, 0, 1773, -3612, 0, 0], [0, -492, 0, 0, 0, 0, 0, -190, 0, 0, -112, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8874, 0, 61668, 0, 0, 348, -2103, 0, 1425, -785, 0, 0], [0, -3698, 0, -3698, 748, 0, 0, -748, 0, 0, -94, 94], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [656, 0, 18608, 0, 0, -2436, -656, 0, -2436, -1312, 0, 0], [0, 0, 0, 4056, -1602, 0, 0, 0, 0, 0, 0, -52], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-72898, 0, 7, 0, 0, 2149, 14, 0, 0, 7, 0, 0], [0, 5194, 0, -5439, 1600, 0, 0, -992, 0, 0, 237, 54], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-63700, 0, -63700, 0, 0, 0, -210, 0, 1146, 210, 0, 0]]}