# Stored data for newform 161.4.c.b, downloaded from the LMFDB on 16 July 2025.
{"Nk2": 2576, "analytic_conductor": 9.49930751092424, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 161, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 3, "char_orbit_label": "c", "char_order": 2, "char_parity": 1, "char_values": [161, 2, [24, 120], [1, 1]], "cm_discs": [], "conrey_index": 160, "dim": 8, "field_disc": 27278068335531361583104, "field_disc_factorization": [[2, 14], [17, 4], [2113, 4]], "field_poly": [23372755, -6463604, -55968, 20128, 43236, -2516, -16, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[2, [1, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503737133432993, "hecke_ring_generator_nbound": 23, "hecke_ring_index": 112, "hecke_ring_index_factorization": [[2, 4], [7, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, 0], [1, 1, 23, 2, -1, 2, 0], [1, 1, 161, 3, 1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "161.4.c.b", "level": 161, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": true, "level_primes": [7, 23], "level_radical": 161, "minimal_twist": "161.4.c.b", "prim_orbit_index": 3, "qexp_display": "q-q^{2}-\\beta _{2}q^{3}-7q^{4}+(-\\beta _{1}-\\beta _{3}+\\cdots)q^{5}+\\cdots", "related_objects": [], "relative_dim": 8, "rm_discs": [], "sato_tate_group": "3.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "161.4.c", "trace_display": [-8, 0, 0, 0], "trace_hash": 920497495913104524, "trace_moments": [{"__RealLiteral__": 0, "data": "0.054", "prec": 17}, {"__RealLiteral__": 0, "data": "6.746", "prec": 17}, {"__RealLiteral__": 0, "data": "1.311", "prec": 17}, {"__RealLiteral__": 0, "data": "466.512", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "43434.061", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.763", "prec": 17}, "traces": [0, 8, -8, 0, -56, 0, 0, 0, 120, -56, 0, 0, 0, 0, 0, 0, 328, 0, 56, 0, 0, 0, 0, -124, 0, 976, 0, 0, 0, 312, 0, 0, -1288, 0, 0, 896, 392, 0, 0, 136, 0, 0, 0, 0, 0, 0, 124, 0, 0, -768, -976, 0, 0, 0, 0, 0, 0, 0, -312, 0, 0, 0, 0, 0, -1336, 0, 0, 0, 0, 0, -896, 3448, -840, 0, 0, 0, 0, -2240, -136, 0, 0, -6952, 0, 0, 0, -1976, 0, 0, 0, 0, 0, 0, 868, 2584, 0, 3264, 0, 0, 768, 0, -6832, 0, 0, 0, 0, 6664, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2184, 0, 0, -896, 0, 7136, 0, 8704, 0, 0, 0, -2432, 11640, 0, 0, 0, 0, -6664, 0, 0, 0, 0, 0, 0, -6272, 10200, -3448, 0, -2296, 0, 0, -3264, 0, 0, 0, -9080, 0, 0, 2240, 0, -952, 0, 0, 0, 0, 5572, 6952, 3744, 0, 3264, 0, 0, 0, 9056, 1976, 0, 0, 0, 0, 0, 0, -12240, 0, 6880, 0, 0, 0, 0, -1860, 0, -2584, 0, 0, 0, -3264, 0, 0, -21512, 0, 0, 5376, -10832, 0, 0, 14640, 0, 0, 0, 0, 0, 0, 868, 0, 0, -6664, -16336, 0, 0, 0, 0, 0, 0, 0, 14960, 0, 0, 0, 0, 0, -6832, 0, 0, 0, 0, 0, -6664, 4680, -27672, 0, 0, 0, 0, 896, 29320, 0, 0, -7136, 0, 0, 0, -8704, 0, 0, 0, 0, 0, 0, 5144, 2432, 0, -952, 0, 0, -11312, 0, -2184, 0, 0, 0, 0, 6664, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3016, 0, 0, 13440, 0, -10200, 0, -24136, 0, 0, 0, 9016, -37328, 0, 0, 0, 0, 3264, 0, 0, 0, 0, 0, 0, -22456, 9080, 55352, 0, 27064, 0, 0, 15680, 0, 0, 0, 2040, 0, 0, -6272, 0, 22712, 0, 0, 0, 0, -5572, -3264, 48664, 0, -3744, 0, 0, 0, -3264, -10032, 0, 0, 0, 0, 0, 0, -9056, 0, 13832, 0, 0, 0, 0, -36856, 0, -48240, 0, 0, 0, 2720, 0, 0, 12240, 0, 0, -6664, -6880, 0, 0, 64536, 0, 0, 0, 0, 0, 0, -5084, 0, 0, 19824, -18088, 0, 0, 0, 0, 0, 0, 0, -22848, 0, 0, 0, 0, 0, 21512, 0, 0, 0, 0, 0, -11520, -44064, 10832, 0, 0, 0, 0, 76160, 40016, 0, 0, 57872, 0, 0, 0, -32104, 0, 0, 0, 0, 0, 0, -868, -7392, 0, -12240, 0, 0, -46648, 0, 16336, 0, 0, 0, 0, 28560, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14960, 0, 0, 5376, 0, -5552, 0, -98712, 0, 0, 0, -18912, 6832, 0, 0, 0, 0, -62496, 0, 0, 0, 0, 0, 0, 6664, 7912, 12792, 0, 27672, 0, 0, -42112, 0, 0, 0, -42392, 0, 0, 6272, 0, -29320, 0, 0, 0, 0, -8568, -49952, 73976, 0, -73536, 0, 0, 0, 27136, -60928, 0, 0, 0, 0, 0, 0, -28400, 0, 70040, 0, 0, 0, 0, -5144, 0, 17024, 0, 0, 0, -92168, 0, 0, 58592, 0, 0, 11312, 62968, 0, 0, 2184, 0, 0, 0, 0, 0, 0, 50192, 0, 0, 46648, -71968, 0, 0, 0, 0, 0, 0, 0, 33816, 0, 0, 0, 0, 0, -37040, 0, 0, 0, 0, 0, 94192, -3016, -98464, 0, 0, 0, 0, 36736, -3264, 0, 0, -71400, 0, 0, 0, 51720, 0, 0, 0, 0, 0, 0, 128556, 9352, 0, 37328, 0, 0, -44072, 0, -12024, 0, 0, 0, 0, 22848, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42816, 0, 0, 22456, 0, 63560, 0, -55352, 0, 0, 0, -27064, 54064, 0, 0, 0, 0, -33600, 0, 0, 0, 0, 0, 0, -20328, 5576, 159440, 0, 119408, 0, 0, 6272, 0, 0, 0, -22712, 0, 0, -65984, 0, -24136, 0, 0, 0, 0, -39004, -24752, 3264, 0, -104280, 0, 0, 0, -26208, -56960, 0, 0, 0, 0, 0, 0, -22848, 0, 10032, 0, 0, 0, 0, -148520, 0, 81464, 0, 0, 0, 119424, 0, 0, -63392, 0, 0, 90552, -29640, 0, 0, 74976, 0, 0, 0, 0, 0, 0, 36856, 0, 0, 15680, 48240, 0, 0, 0, 0, 0, 0, 0, -2720, 0, 0, 0, 0, 0, 85680, 0, 0, 0, 0, 0, 6664, -69248, -48160, 0, 0, 0, 0, 18424, -64536, 0, 0, -249304, 0, 0, 0, -98216, 0, 0, 0, 0, 0, 0, 19964, -8552, 0, 134896, 0, 0, -19824, 0, 38760, 0, 0, 0, 0, 75208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48960, 0, 0, -20048, 0, 13832, 0, 73736, 0, 0, 0, -57392, 150584, 0, 0, 0, 0, -134232, 0, 0, 0, 0, 0, 0, -31488, -27736, 44064, 0, 75824, 0, 0, -14336, 0, 0, 0, -373728, 0, 0, -76160, 0, -157136, 0, 0, 0, 0, -13888, -57872, 53992, 0, -85256, 0, 0, 0, -100776, 32104, 0, 0, 0, 0, 0, 0, -57256, 0, 111936, 0, 0, 0, 0, -6076, 0, 7392, 0, 0, 0, 12240, 0, 0, 51680, 0, 0, 99960, 104424, 0, 0, 114352, 0, 0, 0, 0, 0, 0, -17128, 0, 0, -28560, -22848, 0, 0, 0, 0, 0, 0, 0, 98048, 0, 0, 0, 0, 0, 162048, 0, 0, 0, 0, 0, -2688, -104720, -295592, 0, 0, 0, 0, -5376, 28240, 0, 0, 5552, 0, 0, 0, 98712, 0, 0, 0, 0, 0, 0, 141576, 18912, 0, 47824, 0, 0, -117096, 0, 73640, 0, 0, 0, 0, 62496, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13872, 0, 0, 46648, 0, -7912, 0, -50232, 0, 0, 0, 193704, 113016, 0, 0, 0, 0, 42112, 0, 0, 0, 0, 0, 0, 133280, 42392, 45968, 0, -125808, 0, 0, -13440, 0, 0, 0, -205240, 0, 0, -245952, 0, -200368, 0, 0, 0, 0, 8568, 14760, 107040, 0, -73976, 0, 0, 0, 73536, 303960, 0, 0, 0, 0, 0, 0, -27136, 0, 130560, 0, 0, 0, 0, 30016, 0, -207616, 0, 0, 0, -242944, 0, 0, 28400, 0, 0], "weight": 4, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0], [-7, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, -1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0], [15, 0, 0, 0, 0, 0, 0, 0], [-7, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, -1, 0, 0, 0], [0, 0, 7, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, -1, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, -2, 3, 0, 0, 1], [41, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0], [7, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -6, 3, 0, 0, -1], [0, 7, 0, 7, 0, 0, 0, 0], [0, 0, 0, -7, 1, 0, 0, 0], [0, -1, 0, 0, 1, 0, 0, 0], [-16, -1, 0, -1, 3, 1, 0, 1], [0, 0, -15, 0, 0, 0, 0, 0], [121, 0, 0, 0, 1, 2, 0, 1], [0, 0, -1, 0, 0, 0, 1, 0], [0, 0, -20, 0, 0, 0, 0, 0], [0, 0, 0, 0, 7, 0, 0, 0], [40, 0, 0, 0, -1, -2, 0, -1], [0, 0, 0, 2, -3, 0, 0, -1], [0, 0, 6, 0, 0, 0, 7, 0], [-161, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -6, 3, 0, 0, -1], [0, -1, 0, -1, 0, 0, 0, 0], [112, 0, 28, 0, 0, 0, -7, 0], [49, 0, 0, 0, 0, 0, 0, 0], [0, 11, 0, -4, -5, 0, 0, 2], [0, 0, 0, 6, -3, 0, 0, 1], [16, 0, 0, 0, 1, 2, 0, 1], [0, -15, 0, -15, 0, 0, 0, 0], [0, 0, 36, 0, 0, 0, -8, 0], [0, 0, 0, 7, -1, 0, 0, 0], [0, 13, 0, -2, -10, 0, 0, 1], [0, -7, 0, 0, 7, 0, 0, 0], [0, 7, 0, 7, 0, 0, 0, 0], [16, 1, 0, 1, -3, -1, 0, -1], [0, 0, 34, 0, 0, 0, 7, 0], [0, 0, -41, 0, 0, 0, 0, 0], [-95, 0, -8, 0, -1, -2, -8, -1], [-121, 0, 0, 0, -1, -2, 0, -1], [0, 0, 0, 2, -3, 0, 0, -1], [0, 0, -7, 0, 0, 0, 7, 0], [0, 9, 0, -12, 9, 0, 0, 6], [0, 0, 20, 0, 0, 0, 0, 0], [0, 0, 16, 0, 0, 0, -8, 0], [0, 0, 0, 0, -15, 0, 0, 0], [0, -34, 0, 0, 34, 0, 0, 0], [-40, 0, 0, 0, 1, 2, 0, 1], [0, 0, -49, 0, 0, 0, 8, 0], [0, 0, 0, 14, -21, 0, 0, -7], [0, -17, 0, -5, -6, 0, 0, 2], [0, 0, -6, 0, 0, 0, -7, 0], [0, 0, 0, 0, 7, 0, 0, 0], [-167, 0, 0, 0, 0, 0, 0, 0], [0, 16, 0, 8, -28, 0, 0, -4], [0, 0, 0, 6, -3, 0, 0, 1], [0, -5, 0, 16, -19, 0, 0, -8], [0, -7, 0, -7, 0, 0, 0, 0], [0, 17, 7, 23, -3, 0, 17, 1], [-112, 0, -28, 0, 0, 0, 7, 0], [432, 0, 0, 0, -1, -2, 0, -1], [-105, 0, 0, 0, 0, 0, 0, 0], [0, 0, 62, 0, 0, 0, -14, 0], [0, -11, 0, 4, 5, 0, 0, -2], [0, 0, -139, 0, 0, 0, 34, 0], [0, 0, 0, 42, -21, 0, 0, 7], [-280, 0, -21, 0, 0, 0, -7, 0], [-16, 0, 0, 0, -1, -2, 0, -1], [0, -48, 0, 4, 42, 0, 0, -2], [0, -41, 0, -41, 0, 0, 0, 0], [-869, 0, 0, 0, 0, 0, 0, 0], [0, 0, -36, 0, 0, 0, 8, 0], [0, 12, 0, -18, 15, 0, 0, -5], [0, 0, 0, 49, -7, 0, 0, 0], [-246, 0, 0, 0, -1, -2, 0, -1], [0, -13, 0, 2, 10, 0, 0, -1], [0, 0, -22, 0, 0, 0, -34, 0], [0, 15, 0, 0, -15, 0, 0, 0], [0, 45, 0, 63, -9, 0, 0, 3], [0, -7, 0, -7, 0, 0, 0, 0], [0, 49, 0, 28, -13, 0, 0, 0], [112, 7, 0, 7, -21, -7, 0, -7], [330, 0, 0, 0, -7, -14, 0, -7], [0, 0, -34, 0, 0, 0, -7, 0], [400, 0, 0, 0, 8, 16, 0, 8], [0, 0, 161, 0, 0, 0, 0, 0], [0, -49, 0, -7, -21, 0, 0, 7], [95, 0, 8, 0, 1, 2, 8, 1], [0, -7, 0, 0, 7, 0, 0, 0], [-847, 0, 0, 0, -7, -14, 0, -7]]}