# Stored data for newform 882.3.c.b, downloaded from the LMFDB on 25 April 2024. {"label": "882.3.c.b", "space_label": "882.3.c", "level": 882, "weight": 3, "hecke_orbit": 2, "hecke_orbit_code": 4503737116656498, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.2", "trace_hash": 1193623765164990062, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [144, 0, 72, 0, 1]], [23, [-504, -24, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+2q^{4}+(2\\beta _{2}-2\\beta _{3})q^{5}-2\\beta _{1}q^{8}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 7, "char_orbit_label": "c", "char_is_real": true, "Nk2": 7938, "analytic_conductor": 24.032759316578186, "hecke_ring_index": 4, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [882, 2, [785, 199], [2, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [685], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, 2, 0, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.719", "prec": 17}, {"__RealLiteral__": 0, "data": "1.085", "prec": 17}, {"__RealLiteral__": 0, "data": "66.588", "prec": 20}, {"__RealLiteral__": 0, "data": "55.840", "prec": 20}, {"__RealLiteral__": 0, "data": "1638.679", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, 8, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 48, 0, -44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, 28, -48, 0, 144, 0, 0, 0, 192, 0, 0, 240, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 32, 360, 0, -220, 0, 0, 0, -312, 0, 0, -96, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -288, -48, 0, 0, 0, 0, 0, 96, 0, 0, -264, 0, 0, 0, 0, -88, 0, 0, 0, 0, 0, 144, -576, 0, 580, 0, 0, 0, -168, 0, 0, 0, 0, 0, 0, 0, -340, 0, 0, 0, 0, 0, 500, 0, 0, -336, 0, 0, 0, 336, 0, 0, -336, 0, 0, 0, 0, -336, 0, 0, 0, 0, 0, -88, -528, 0, -680, 0, 0, 0, -120, 0, 0, 528, 0, 0, 0, 0, 200, 0, 0, 0, 0, 0, -872, 480, 0, 56, 0, 0, 0, -96, 0, 0, -168, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, 432, -504, 0, 436, 0, 0, 0, 288, 0, 0, 384, 0, 0, 0, 0, 432, 0, 0, 0, 0, 0, -296, 480, 0, 144, 0, 0, 0, -192, 0, 0, 288, 0, 0, 0, 0, -336, 0, 0, 0, 0, 0, 384, 984, 0, 432, 0, 0, 0, -1128, 0, 0, 0, 0, 0, 0, 0, 300, 0, 0, 0, 0, 0, -288, -240, 0, 64, 0, 0, 0, 720, 0, 0, -384, 0, 0, 0, 0, -440, 0, 0, 0, 0, 0, 96, 264, 0, -820, 0, 0, 0, 384, 0, 0, -624, 0, 0, 0, 0, 292, 0, 0, 0, 0, 0, 576, -192, 0, 288, 0, 0, 0, 672, 0, 0, -672, 0, 0, 0, 0, 528, 0, 0, 0, 0, 0, 40, 240, 0, 0, 0, 0, 0, -768, 0, 0, 192, 0, 0, 0, 0, -740, 0, 0, 0, 0, 0, 1156, -384, 0, -576, 0, 0, 0, -96, 0, 0, 576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -720, -624, 0, 760, 0, 0, 0, 2184, 0, 0, 192, 0, 0, 0, 0, -1300, 0, 0, 0, 0, 0, -836, -528, 0, 336, 0, 0, 0, -672, 0, 0, 2424, 0, 0, 0, 0, 1104, 0, 0, 0, 0, 0, -176, 1680, 0, -1356, 0, 0, 0, 264, 0, 0, -1056, 0, 0, 0, 0, 1584, 0, 0, 0, 0, 0, -340, 288, 0, 288, 0, 0, 0, -1152, 0, 0, -216, 0, 0, 0, 0, 1160, 0, 0, 0, 0, 0, -1488, 576, 0, 288, 0, 0, 0, -1464, 0, 0, -336, 0, 0, 0, 0, -908, 0, 0, 0, 0, 0, 932, 0, 0, -48, 0, 0, 0, -960, 0, 0, -168, 0, 0, 0, 0, -480, 0, 0, 0, 0, 0, -680, -480, 0, 28, 0, 0, 0, 336, 0, 0, -1296, 0, 0, 0, 0, -1316, 0, 0, 0, 0, 0, 2448, -864, 0, 1000, 0, 0, 0, 0, 0, 0, -1656, 0, 0, 0, 0, -672, 0, 0, 0, 0, 0, 1056, -1344, 0, 1052, 0, 0, 0, 1080, 0, 0, 672, 0, 0, 0, 0, 476, 0, 0, 0, 0, 0, 104, -672, 0, -1152, 0, 0, 0, -384, 0, 0, 2712, 0, 0, 0, 0, -1296, 0, 0, 0, 0, 0, -672, -1512, 0, 500, 0, 0, 0, 2928, 0, 0, 768, 0, 0, 0, 0, -1440, 0, 0, 0, 0, 0, -1140, -480, 0, -176, 0, 0, 0, -1056, 0, 0, -2544, 0, 0, 0, 0, -1360, 0, 0, 0, 0, 0, 960, 648, 0, -2248, 0, 0, 0, -1176, 0, 0, -240, 0, 0, 0, 0, 1492, 0, 0, 0, 0, 0, -2392, 1056, 0, -192, 0, 0, 0, -1152, 0, 0, 0, 0, 0, 0, 0, 720, 0, 0, 0, 0, 0, 400, -2232, 0, -144, 0, 0, 0, 384, 0, 0, 432, 0, 0, 0, 0, 3456, 0, 0, 0, 0, 0, 916, 864, 0, -1744, 0, 0, 0, 960, 0, 0, -1776, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, -1008, 2088, 0, 2304, 0, 0, 0, 1392, 0, 0, -192, 0, 0, 0, 0, 2920, 0, 0, 0, 0, 0, -2160, -336, 0, -768, 0, 0, 0, 672, 0, 0, 4608, 0, 0, 0, 0, -2448, 0, 0, 0, 0, 0, 576, 1320, 0, 1076, 0, 0, 0, 456, 0, 0, 2016, 0, 0, 0, 0, -1940, 0, 0, 0, 0, 0, 2104, 2352, 0, 864, 0, 0, 0, -1008, 0, 0, -2736, 0, 0, 0, 0, 872, 0, 0, 0, 0, 0, 240, 1992, 0, 1872, 0, 0, 0, -2592, 0, 0, 576, 0, 0, 0, 0, 1392, 0, 0, 0, 0, 0, 2016, 768, 0, 816, 0, 0, 0, -3408, 0, 0, 408, 0, 0, 0, 0, 576, 0, 0, 0, 0, 0, 864, 840, 0, -2008, 0, 0, 0, 3192, 0, 0, -1344, 0, 0, 0, 0, -3312, 0, 0, 0, 0, 0, 1244, 672, 0, -592, 0, 0, 0, 960, 0, 0, -2256, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, -2544, -2760, 0, 3456, 0, 0, 0, -120, 0, 0, -384, 0, 0, 0, 0, 1304, 0, 0, 0, 0, 0, 748, 576, 0, 144, 0, 0, 0, -576, 0, 0, 1752, 0, 0, 0, 0, 1968, 0, 0, 0, 0, 0, -672, 696, 0, -452, 0, 0, 0, 1920, 0, 0, -576, 0, 0, 0, 0, -2948, 0, 0, 0, 0, 0, -1820, -3600, 0, 768, 0, 0, 0, 1968, 0, 0, 1728, 0, 0, 0, 0, 864, 0, 0, 0, 0, 0, 288, -648, 0, -7548, 0, 0, 0, -2112, 0, 0, -2256, 0, 0, 0, 0, -488, 0, 0, 0, 0, 0, -1372, 0, 0, 768, 0, 0, 0, 3216, 0, 0, 2280, 0, 0, 0, 0, -1824, 0, 0, 0, 0, 0, 600, -528, 0, -1124, 0, 0, 0, -480, 0, 0, 240, 0, 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, 7, 2, -1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 2, "minimal_twist": "42.3.g.a", "char_is_minimal": true, "conrey_index": 685, "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], [1, 0, 0, 0], [0, -1, 0, 0], [0, 0, 0, 0], [2, 0, 0, 0], [0, 0, 2, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2, 0, 0], [0, 0, 0, 0], [0, 0, -4, 2], [-6, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 8], [0, 0, 0, 0], [0, 0, 0, 0], [4, 0, 0, 0], [0, 0, 8, -2], [0, 0, 0, 0], [0, 0, 7, -2], [0, 0, 4, -4], [0, 0, 0, 0], [0, 6, 0, 0], [12, -18, 0, 0], [0, 0, 0, 0], [-11, -24, 0, 0], [0, 0, 16, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, -24, 0, 0], [0, 0, 0, 0], [0, 0, 17, 6], [0, -4, 0, 0], [0, 0, 0, 0], [0, 0, -4, 8], [0, 0, 0, 0], [0, 0, 0, 0], [-11, 12, 0, 0], [0, 0, -4, 7], [0, 0, 0, 0], [0, 0, -8, 4], [0, 0, -26, -4], [0, 0, 0, 0], [7, 6, 0, 0], [-12, 0, 0, 0], [0, 0, 0, 0], [36, -12, 0, 0], [0, 0, -22, -2], [0, 0, 0, 0], [0, 0, 0, 0], [48, 11, 0, 0], [0, 0, 0, 0], [0, 0, 2, 16], [60, -18, 0, 0], [0, 0, 0, 0], [0, 0, -12, 12], [0, 0, 0, 0], [0, 0, 0, 0], [48, 0, 0, 0], [0, 0, 4, 14], [0, 0, 0, 0], [0, 0, 12, -8], [0, 0, 12, 17], [0, 0, 0, 0], [8, 0, 0, 0], [90, 42, 0, 0], [0, 0, 0, 0], [-55, -42, 0, 0], [0, 0, 16, -4], [0, 0, 0, 0], [0, 0, 0, 0], [-78, 42, 0, 0], [0, 0, 0, 0], [0, 0, -11, 40], [-24, 11, 0, 0], [0, 0, 0, 0], [0, 0, 14, -4], [0, 0, 0, 0], [0, 0, 0, 0], [5, -66, 0, 0], [0, 0, 8, -8], [0, 0, 0, 0], [0, 0, -8, -26], [0, 0, 10, 38], [0, 0, 0, 0], [-72, -60, 0, 0], [-12, -7, 0, 0], [0, 0, 0, 0], [0, 12, 0, 0], [0, 0, -12, 0], [0, 0, 0, 0], [0, 0, 0, 0], [24, -36, 0, 0], [0, 0, 0, 0], [0, 0, -4, -22], [-66, -54, 0, 0], [0, 0, 0, 0], [0, 0, 12, -4], [0, 0, 0, 0], [0, 0, 0, 0], [-22, -48, 0, 0]]}