# Stored data for newform 768.6.d.c, downloaded from the LMFDB on 19 April 2024. {"label": "768.6.d.c", "space_label": "768.6.d", "level": 768, "weight": 6, "hecke_orbit": 3, "hecke_orbit_code": 9007405513835264, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 1096292389889628644, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [4356, 0, 1]], [7, [176, 1]]], "qexp_display": "q-9iq^{3}+66iq^{5}-176q^{7}-3^{4}q^{9}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 8, "char_orbit_label": "d", "char_is_real": true, "Nk2": 27648, "analytic_conductor": 123.17477361636912, "hecke_ring_index": 1, "level_radical": 6, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": "0.507", "prec": 17}, "analytic_rank_proved": true, "char_values": [768, 2, [511, 517, 257], [2, 1, 2]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [385], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.052", "prec": 17}, {"__RealLiteral__": 0, "data": "1.920", "prec": 17}, {"__RealLiteral__": 0, "data": "0.668", "prec": 17}, {"__RealLiteral__": 0, "data": "15.613", "prec": 20}, {"__RealLiteral__": 0, "data": "10.053", "prec": 20}, {"__RealLiteral__": 0, "data": "161.201", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "5.2.3.c2", "trace_display": [0, 0, 0, -352], "traces": [0, 2, 0, 0, 0, 0, 0, -352, 0, -162, 0, 0, 0, 0, 0, 1188, 0, -828, 0, 0, 0, 0, 0, -1200, 0, -2462, 0, 0, 0, 0, 0, -7184, 0, 1080, 0, 0, 0, 0, 0, -11844, 0, -38388, 0, 0, 0, 0, 0, -39360, 0, 28338, 0, 0, 0, 0, 0, -7920, 0, 17208, 0, 0, 0, 0, 0, 28512, 0, 86856, 0, 0, 0, 0, 0, -12240, 0, 51116, 0, 0, 0, 0, 0, 148816, 0, 13122, 0, 0, 0, 0, 0, 100332, 0, 65484, 0, 0, 0, 0, 0, -126192, 0, 332164, 0, 0, 0, 0, 0, 158528, 0, -209088, 0, 0, 0, 0, 0, 152244, 0, -390876, 0, 0, 0, 0, 0, 145728, 0, 314902, 0, 0, 0, 0, 0, 346000, 0, -239688, 0, 0, 0, 0, 0, -96228, 0, 256908, 0, 0, 0, 0, 0, 78960, 0, -735768, 0, 0, 0, 0, 0, 407744, 0, 67068, 0, 0, 0, 0, 0, 562788, 0, 211200, 0, 0, 0, 0, 0, 1352400, 0, -123342, 0, 0, 0, 0, 0, 433312, 0, -474120, 0, 0, 0, 0, 0, -559620, 0, -1116456, 0, 0, 0, 0, 0, -530688, 0, 590596, 0, 0, 0, 0, 0, -1304896, 0, -302472, 0, 0, 0, 0, 0, 97200, 0, -114720, 0, 0, 0, 0, 0, 1757712, 0, 1264384, 0, 0, 0, 0, 0, 1403920, 0, 199422, 0, 0, 0, 0, 0, -190080, 0, 877356, 0, 0, 0, 0, 0, 56928, 0, 1785124, 0, 0, 0, 0, 0, 1258096, 0, -116424, 0, 0, 0, 0, 0, -491832, 0, 281604, 0, 0, 0, 0, 0, 1877520, 0, -4127112, 0, 0, 0, 0, 0, 1135408, 0, 2084544, 0, 0, 0, 0, 0, 581904, 0, -1375476, 0, 0, 0, 0, 0, 6756288, 0, -2496922, 0, 0, 0, 0, 0, 3476880, 0, -87480, 0, 0, 0, 0, 0, 396036, 0, 4103880, 0, 0, 0, 0, 0, 3004080, 0, -1621684, 0, 0, 0, 0, 0, -668880, 0, -4103784, 0, 0, 0, 0, 0, -153540, 0, 6927360, 0, 0, 0, 0, 0, 2218128, 0, -5504348, 0, 0, 0, 0, 0, 928576, 0, -712800, 0, 0, 0, 0, 0, 959364, 0, -1244028, 0, 0, 0, 0, 0, -7481232, 0, 3124326, 0, 0, 0, 0, 0, 32464, 0, 3109428, 0, 0, 0, 0, 0, 2250072, 0, 7335384, 0, 0, 0, 0, 0, -5959680, 0, 1393920, 0, 0, 0, 0, 0, 496800, 0, 2722680, 0, 0, 0, 0, 0, -3028608, 0, 10882308, 0, 0, 0, 0, 0, -1014960, 0, -3939892, 0, 0, 0, 0, 0, 853776, 0, -2775528, 0, 0, 0, 0, 0, 3188160, 0, 1019268, 0, 0, 0, 0, 0, -5598720, 0, -11804828, 0, 0, 0, 0, 0, 893024, 0, -2295378, 0, 0, 0, 0, 0, -530172, 0, -2412252, 0, 0, 0, 0, 0, -15286656, 0, -467092, 0, 0, 0, 0, 0, -5835728, 0, -4267296, 0, 0, 0, 0, 0, 2450556, 0, 1597920, 0, 0, 0, 0, 0, 4689312, 0, 11130728, 0, 0, 0, 0, 0, -19630624, 0, -3080232, 0, 0, 0, 0, 0, 641520, 0, 2154240, 0, 0, 0, 0, 0, -9435888, 0, -2904264, 0, 0, 0, 0, 0, -8996416, 0, -1393848, 0, 0, 0, 0, 0, 2396844, 0, -16039476, 0, 0, 0, 0, 0, 2974176, 0, -12152686, 0, 0, 0, 0, 0, 30094416, 0, -12481128, 0, 0, 0, 0, 0, -6789132, 0, 1125960, 0, 0, 0, 0, 0, -10657488, 0, -26191616, 0, 0, 0, 0, 0, -17523856, 0, -447120, 0, 0, 0, 0, 0, -2309472, 0, 10926444, 0, 0, 0, 0, 0, 1477200, 0, 31887364, 0, 0, 0, 0, 0, -3751920, 0, -7035336, 0, 0, 0, 0, 0, -3623292, 0, 4906980, 0, 0, 0, 0, 0, 18599568, 0, 22923404, 0, 0, 0, 0, 0, 22556752, 0, -17658432, 0, 0, 0, 0, 0, -22802472, 0, 29928300, 0, 0, 0, 0, 0, -11525184, 0, -24194278, 0, 0, 0, 0, 0, -31183744, 0, -20647080, 0, 0, 0, 0, 0, 991440, 0, 21940260, 0, 0, 0, 0, 0, 12113712, 0, 3160800, 0, 0, 0, 0, 0, -19966320, 0, -4140396, 0, 0, 0, 0, 0, 4903416, 0, 22209792, 0, 0, 0, 0, 0, 3730800, 0, 2845252, 0, 0, 0, 0, 0, -58460864, 0, 22249944, 0, 0, 0, 0, 0, -1904940, 0, 41146056, 0, 0, 0, 0, 0, 20353872, 0, 15892632, 0, 0, 0, 0, 0, -16171696, 0, -23379840, 0, 0, 0, 0, 0, -12054096, 0, 4310400, 0, 0, 0, 0, 0, -52784640, 0, -27900928, 0, 0, 0, 0, 0, 19589696, 0, -1062882, 0, 0, 0, 0, 0, 16832772, 0, 2016480, 0, 0, 0, 0, 0, -28828272, 0, 3887928, 0, 0, 0, 0, 0, 33588880, 0, 1982232, 0, 0, 0, 0, 0, -648000, 0, 4295724, 0, 0, 0, 0, 0, -34663440, 0, -26211836, 0, 0, 0, 0, 0, 8843504, 0, -26794944, 0, 0, 0, 0, 0, -8126892, 0, -17970744, 0, 0, 0, 0, 0, 68794176, 0, -40914440, 0, 0, 0, 0, 0, 16295040, 0, -5304204, 0, 0, 0, 0, 0, -20061108, 0, 52155468, 0, 0, 0, 0, 0, 22588368, 0, 25460192, 0, 0, 0, 0, 0, 31257920, 0, -1329480, 0, 0, 0, 0, 0, 21838644, 0, -11731932, 0, 0, 0, 0, 0, -60780048, 0, -21116654, 0, 0, 0, 0, 0, -55422752, 0, 14956344, 0, 0, 0, 0, 0, 10221552, 0, -17282004, 0, 0, 0, 0, 0, 78038208, 0, -17576856, 0, 0, 0, 0, 0, -22114064, 0, -26905284, 0, 0, 0, 0, 0, 23627268, 0, 61062372, 0, 0, 0, 0, 0, 26830320, 0, -60896000, 0, 0, 0, 0, 0, 91528272, 0, 7106400, 0, 0, 0, 0, 0, 42185088, 0, 49786968, 0, 0, 0, 0, 0, 2380704, 0, 776160, 0, 0, 0, 0, 0, 94399232, 0, 30423960, 0, 0, 0, 0, 0, -12840768, 0, 2671908, 0, 0, 0, 0, 0, 3278880, 0, -29447572, 0, 0, 0, 0, 0, 23032800, 0, 16936128, 0, 0, 0, 0, 0, 16264044, 0, -43747092, 0, 0, 0, 0, 0, -45215808, 0, -31453374, 0, 0, 0, 0, 0, -35204992, 0, -7124112, 0, 0, 0, 0, 0, 14579964, 0, 111076356, 0, 0, 0, 0, 0, 77356848, 0, 26570808, 0, 0, 0, 0, 0, 19169968, 0, -20195496, 0, 0, 0, 0, 0, -12331764, 0], "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, 8, 2, 1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 2, "minimal_twist": "6.6.a.a", "char_is_minimal": false, "conrey_index": 385, "id": 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], [1, 0], [0, 0], [0, -9], [0, 0], [0, 66], [0, 0], [-176, 0], [0, 0], [-81, 0], [0, 0], [0, 60], [0, 0], [0, -658], [0, 0], [594, 0], [0, 0], [-414, 0], [0, 0], [0, 956], [0, 0], [0, 1584], [0, 0], [-600, 0], [0, 0], [-1231, 0], [0, 0], [0, 729], [0, 0], [0, 5574], [0, 0], [-3592, 0], [0, 0], [540, 0], [0, 0], [0, -11616], [0, 0], [0, 8458], [0, 0], [-5922, 0], [0, 0], [-19194, 0], [0, 0], [0, -13316], [0, 0], [0, -5346], [0, 0], [-19680, 0], [0, 0], [14169, 0], [0, 0], [0, 3726], [0, 0], [0, 31266], [0, 0], [-3960, 0], [0, 0], [8604, 0], [0, 0], [0, -26340], [0, 0], [0, -31090], [0, 0], [14256, 0], [0, 0], [43428, 0], [0, 0], [0, -16804], [0, 0], [0, 5400], [0, 0], [-6120, 0], [0, 0], [25558, 0], [0, 0], [0, 11079], [0, 0], [0, -10560], [0, 0], [74408, 0], [0, 0], [6561, 0], [0, 0], [0, -6468], [0, 0], [0, -27324], [0, 0], [50166, 0], [0, 0], [32742, 0], [0, 0], [0, 115808], [0, 0], [0, 32328], [0, 0], [-63096, 0], [0, 0], [166082, 0], [0, 0], [0, -4860], [0, 0]]}