# Stored data for newform 1764.3.bk.d, downloaded from the LMFDB on 16 April 2024.
{"label": "1764.3.bk.d", "space_label": "1764.3.bk", "level": 1764, "weight": 3, "hecke_orbit": 4, "hecke_orbit_code": 13513272833607396, "dim": 8, "is_polredabs": true, "nf_label": "8.0.12745506816.5", "trace_hash": 2006592421412880583, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [20736, 0, -4608, 0, 880, 0, -32, 0, 1]], [13, [-108, 4, 1]]], "qexp_display": "q+\\beta _{1}q^{5}+(2\\beta _{5}-\\beta _{7})q^{11}+(-2-2\\beta _{3}+\\cdots)q^{13}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 21, "char_orbit_label": "bk", "char_is_real": false, "Nk2": 15876, "analytic_conductor": 48.06551863315637, "hecke_ring_index": 144, "level_radical": 42, "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": "0.510", "prec": 17}, "analytic_rank_proved": true, "char_values": [1764, 6, [883, 785, 1081], [6, 3, 4]], "hecke_ring_generator_nbound": 25, "inner_twist_count": 4, "level_primes": [2, 3, 7], "conrey_indexes": [557, 1745], "field_disc": 12745506816, "field_disc_factorization": [[2, 16], [3, 4], [7, 4]], "field_poly": [81, 0, -72, 0, 55, 0, -8, 0, 1], "hecke_ring_index_factorization": [[2, 4], [3, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.209", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "380.376", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "37213.864", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c6", "trace_display": [0, 0, 0, 0], "traces": [0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -208, 0, 0, 0, 0, 0, 272, 0, 0, 0, 0, 0, -168, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, -232, 0, 0, 0, 0, 0, -544, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 328, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, -252, 0, 0, 0, 0, 0, -688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -768, 0, 0, 0, 0, 0, 664, 0, 0, 0, 0, 0, -432, 0, 0, 0, 0, 0, -464, 0, 0, 0, 0, 0, -488, 0, 0, 0, 0, 0, -424, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 272, 0, 0, 0, 0, 0, 568, 0, 0, 0, 0, 0, -320, 0, 0, 0, 0, 0, -320, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1088, 0, 0, 0, 0, 0, 648, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 208, 0, 0, 0, 0, 0, -752, 0, 0, 0, 0, 0, -560, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 528, 0, 0, 0, 0, 0, 104, 0, 0, 0, 0, 0, -872, 0, 0, 0, 0, 0, -312, 0, 0, 0, 0, 0, 252, 0, 0, 0, 0, 0, 1888, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1392, 0, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, 1016, 0, 0, 0, 0, 0, -376, 0, 0, 0, 0, 0, 640, 0, 0, 0, 0, 0, -1792, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2688, 0, 0, 0, 0, 0, -1048, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 1552, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, 576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1232, 0, 0, 0, 0, 0, -1072, 0, 0, 0, 0, 0, 304, 0, 0, 0, 0, 0, -704, 0, 0, 0, 0, 0, -928, 0, 0, 0, 0, 0, 560, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1456, 0, 0, 0, 0, 0, -1216, 0, 0, 0, 0, 0, 1056, 0, 0, 0, 0, 0, 312, 0, 0, 0, 0, 0, 1920, 0, 0, 0, 0, 0, 624, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 624, 0, 0, 0, 0, 0, -1280, 0, 0, 0, 0, 0, 2128, 0, 0, 0, 0, 0, 2696, 0, 0, 0, 0, 0, 336, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1920, 0, 0, 0, 0, 0, -1952, 0, 0, 0, 0, 0, -1500, 0, 0, 0, 0, 0, -1656, 0, 0, 0, 0, 0, 1592, 0, 0, 0, 0, 0, 7184, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2624, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 1736, 0, 0, 0, 0, 0, -696, 0, 0, 0, 0, 0, 264, 0, 0, 0, 0, 0, -1472, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5200, 0, 0, 0, 0, 0, -2320, 0, 0, 0, 0, 0, 776, 0, 0, 0, 0, 0, 4512, 0, 0, 0, 0, 0, 828, 0, 0, 0, 0, 0, -176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5072, 0, 0, 0, 0, 0, -1408, 0, 0, 0, 0, 0, 1312, 0, 0, 0, 0, 0, -2400, 0, 0, 0, 0, 0, 392, 0, 0, 0, 0, 0, 4576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2128, 0, 0, 0, 0, 0, -320, 0, 0, 0, 0, 0, 816, 0, 0, 0, 0, 0, -1696, 0, 0, 0, 0, 0, 2320, 0, 0, 0, 0, 0, 864, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1200, 0, 0, 0, 0, 0, -904, 0, 0, 0, 0, 0, -184, 0, 0, 0, 0, 0, 3144, 0, 0, 0, 0, 0, -2272, 0, 0, 0, 0, 0, -2464, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 816, 0, 0, 0, 0, 0, -136, 0, 0, 0, 0, 0, -2648, 0, 0, 0, 0, 0, -496, 0, 0, 0, 0, 0, -320, 0, 0, 0, 0, 0, 3936, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -960, 0, 0, 0, 0, 0, 1856, 0, 0, 0, 0, 0, 2424, 0, 0, 0, 0, 0, -1512, 0, 0, 0, 0, 0, 2128, 0, 0, 0, 0, 0, -7176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2368, 0, 0, 0, 0, 0, -1352, 0, 0, 0, 0, 0, 2800, 0, 0, 0, 0, 0, 3472, 0, 0, 0, 0, 0, -1512, 0, 0, 0, 0, 0, -608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5328, 0, 0, 0, 0, 0, 264, 0, 0, 0, 0, 0, -4816, 0, 0, 0, 0, 0, -2768, 0, 0, 0, 0, 0, -3600, 0, 0, 0, 0, 0, 3264, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3856, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, -744, 0, 0, 0, 0, 0, 3332, 0, 0, 0, 0, 0, -8912, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1104, 0, 0, 0, 0, 0, 2792, 0, 0, 0, 0, 0, -944, 0, 0, 0, 0, 0, 2704, 0, 0, 0, 0, 0, -3760, 0, 0, 0, 0, 0, -3824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1152, 0, 0, 0, 0, 0, 4048, 0, 0, 0, 0, 0, -4360, 0, 0, 0, 0, 0, -5920, 0, 0, 0, 0, 0, -1376, 0, 0, 0, 0, 0, 6224, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12656, 0, 0, 0, 0, 0, 5200, 0, 0, 0, 0, 0, 1488, 0, 0, 0, 0, 0, -2688, 0, 0, 0, 0, 0, 1544, 0, 0, 0, 0, 0, -2736, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2880, 0, 0, 0, 0, 0, 1160, 0, 0, 0, 0, 0, -544, 0, 0, 0, 0, 0, 7504, 0, 0, 0, 0, 0, -3832, 0, 0, 0, 0, 0, -3936, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -704, 0, 0, 0, 0, 0, -480, 0, 0, 0, 0, 0, -2384, 0, 0, 0, 0, 0, -5560, 0, 0, 0, 0, 0, -1728, 0, 0, 0, 0, 0, 2736, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3984, 0, 0, 0, 0, 0, 3336, 0, 0, 0, 0, 0, -2000, 0, 0, 0, 0, 0, -6344, 0, 0, 0, 0, 0, -168, 0, 0, 0, 0, 0, -3696, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7904, 0, 0, 0, 0, 0, 3112, 0, 0, 0, 0, 0, -1432, 0, 0, 0, 0, 0, 4736, 0, 0, 0, 0, 0, -2064, 0, 0, 0, 0, 0, -8000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12768, 0, 0, 0, 0, 0, 3664, 0, 0, 0, 0, 0, -4896, 0, 0, 0, 0, 0, -2408, 0, 0, 0, 0, 0, -1304, 0, 0, 0, 0, 0, 5216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2256, 0, 0, 0, 0, 0, 7000, 0, 0, 0, 0, 0, 912, 0, 0, 0, 0, 0, -512, 0, 0, 0, 0, 0, 4048, 0, 0, 0, 0, 0, -3008, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 896, 0, 0, 0, 0, 0, 384, 0, 0, 0, 0, 0, 1188, 0, 0, 0, 0, 0, 3312, 0, 0, 0, 0, 0, -624, 0, 0, 0, 0, 0, -2208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2832, 0, 0, 0, 0, 0, -4408, 0, 0, 0, 0, 0, -6464, 0, 0, 0, 0, 0, -5792, 0, 0, 0, 0, 0, -4992, 0, 0, 0, 0, 0, 8128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1280, 0, 0, 0, 0, 0, -616, 0, 0, 0, 0, 0, 6032, 0, 0, 0, 0, 0, -456, 0, 0, 0, 0, 0, -3408, 0, 0, 0, 0, 0, -15264, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4624, 0, 0, 0, 0, 0, -2160, 0, 0, 0, 0, 0, 1008, 0, 0, 0, 0, 0, 7696, 0, 0, 0, 0, 0, 728, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5344, 0, 0, 0, 0, 0, 5392, 0, 0, 0, 0, 0, -3432, 0, 0, 0, 0, 0, -7616, 0, 0, 0, 0, 0, 1184, 0, 0, 0, 0, 0, 7840, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1648, 0, 0, 0, 0, 0, 1400, 0, 0, 0, 0, 0, 1960, 0, 0, 0, 0, 0, -360, 0, 0, 0, 0, 0, 4160, 0, 0, 0, 0, 0, -10176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6432, 0, 0, 0, 0, 0, -4064, 0, 0, 0, 0, 0, 712, 0, 0, 0, 0, 0, 11864, 0, 0, 0, 0, 0, -3752, 0, 0, 0, 0, 0, -13872, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13024, 0, 0, 0, 0, 0, -5624, 0, 0, 0, 0, 0, 3528, 0, 0, 0, 0, 0, -3000, 0, 0, 0, 0, 0, 1624, 0, 0, 0, 0, 0, 12296, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7008, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 1152, 0, 0, 0, 0, 0, -9920, 0, 0, 0, 0, 0, 2336, 0, 0, 0, 0, 0, 15024, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -528, 0, 0, 0, 0, 0, -4000, 0, 0, 0, 0, 0, -2048, 0, 0, 0, 0, 0, 7952, 0, 0, 0, 0, 0, 448, 0, 0, 0, 0, 0, 12576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10464, 0, 0, 0, 0, 0, -3208, 0, 0, 0, 0, 0, -2176, 0, 0, 0, 0, 0, 3256, 0, 0, 0, 0, 0, 5568, 0, 0, 0, 0, 0, 3328, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8784, 0, 0, 0, 0, 0, -1520, 0, 0, 0, 0, 0, 4712, 0, 0, 0, 0, 0, 1568, 0, 0, 0, 0, 0, 6672, 0, 0, 0, 0, 0, -6600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3520, 0, 0, 0, 0, 0, -496, 0, 0, 0, 0, 0, 10688, 0, 0, 0, 0, 0, -776, 0, 0, 0, 0, 0, -6480, 0, 0, 0, 0, 0, -5216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2800, 0, 0, 0, 0, 0, -4592, 0, 0, 0, 0, 0, -3616, 0, 0, 0, 0, 0, -2776, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 13456, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12752, 0, 0, 0, 0, 0, -3632, 0, 0, 0, 0, 0, 3776, 0, 0, 0, 0, 0, 4000, 0, 0, 0, 0, 0, 6408, 0, 0, 0, 0, 0, -2992, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27680, 0, 0, 0, 0, 0, -6504, 0, 0, 0, 0, 0, 120, 0], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0], [1, 1, 21, 8, -1, 6, 0], [1, 1, 3, 2, -1, 2, 0]], "char_orbit_index": 37, "prim_orbit_index": 8, "minimal_twist": "252.3.c.a", "char_is_minimal": false, "conrey_index": 557, "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, 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, 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, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 5, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 10, 0, 0, 0, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, -3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-9, 0, 9, 2, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -10, 0, 0, -1, -10, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-10, 0, 10, -1, 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, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -8, 0, 0, 0, -6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, 0, 0, -3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 0, 6, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -6, 0, 0, 14, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0], [-26, 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, 0, 0, 0, 0], [0, 0, 0, 0, 0, -14, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 68, 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, 0], [0, -6, 0, 0, -8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-42, 0, 42, -14, 0, 0, -14, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 22, 0, 0, -15, 22, 0, -15], [0, 0, 0, 0, 0, 0, 0, 0], [-36, 0, 36, 1, 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, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -58, 0, 0, 0, 16, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 22, 0, 0, -20, 22, 0, -20], [0, 0, 0, 0, 0, 0, 0, 0], [-68, 0, 0, -4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 36, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -16, 0, -12], [0, 0, 0, 0, 0, 0, 0, 0], [24, 0, 0, 17, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}