# Stored data for newform 504.2.bk.a, downloaded from the LMFDB on 25 April 2024. {"label": "504.2.bk.a", "space_label": "504.2.bk", "level": 504, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 2473934717432, "dim": 12, "is_polredabs": true, "nf_label": "12.0.144054149089536.2", "trace_hash": 1108678034298882541, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [441, 0, 1071, 0, 2286, 0, 723, 0, 174, 0, 15, 0, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+(-\\beta _{3}+\\beta _{9}-\\beta _{10}+\\beta _{11})q^{4}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 56, "char_orbit_label": "bk", "char_is_real": false, "Nk2": 2016, "analytic_conductor": 4.024460261872531, "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": "0.596", "prec": 17}, "analytic_rank_proved": true, "char_values": [504, 6, [127, 253, 281, 73], [3, 3, 6, 5]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [2, 3, 7], "conrey_indexes": [19, 451], "field_disc": 144054149089536, "field_disc_factorization": [[2, 8], [3, 14], [7, 6]], "field_poly": [4, -12, 96, -340, 624, -654, 431, -189, 48, 1, 0, -3, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.004", "prec": 17}, {"__RealLiteral__": 0, "data": "10.779", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "881.262", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "104964.503", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 0, 0, 0], "traces": [0, 12, 0, 0, 0, 0, 0, 0, 12, 0, 6, 6, 0, 0, -6, 0, 0, 6, 0, -6, 0, 0, 24, 0, 0, 0, -6, 0, 6, 0, 0, 0, 0, 0, 0, -18, 0, 0, 24, 0, 42, 0, 0, 0, -6, 0, -18, 0, 0, -12, 48, 0, -24, 0, 0, 0, 0, 0, 18, -42, 0, 0, 0, 0, -72, 12, 0, 30, 36, 0, 30, 0, 0, 18, -12, 0, 0, 0, 0, 0, -36, 0, 54, 0, 0, 0, 0, 0, 6, -18, 0, -72, -60, 0, -12, 0, 0, 0, 6, 0, -12, 0, 0, 0, 0, 0, -96, 18, 0, 0, 30, 0, -48, -24, 0, -102, 12, 0, 0, 0, 0, 36, -72, 0, -66, 0, 0, 0, 0, 0, 18, 42, 0, 0, -60, 0, 6, 18, 0, 0, -12, 0, 0, 0, 0, 24, 0, 0, 72, 0, 0, 0, -6, 0, -6, -60, 0, 0, 6, 0, 0, 18, 0, 18, 36, 0, -60, 0, 0, -12, 36, 0, 0, 0, 0, 0, 24, 0, 0, -66, 0, 0, -6, 0, 42, 30, 0, 66, 0, 0, 84, 0, 0, 6, 6, 0, 48, 0, 0, 0, 0, 0, 0, 96, 0, 0, 66, 0, 36, 0, 0, 0, -24, 0, -24, 0, 0, -6, 36, 0, -6, 0, 0, 0, -36, 0, 18, 90, 0, 0, 0, 0, 0, 42, 0, -66, -54, 0, -6, 0, 0, -30, 18, 0, 0, 0, 0, 0, -42, 0, 78, 0, 0, 0, -36, 0, 0, 6, 0, 138, 24, 0, -6, 0, 0, 0, -42, 0, -6, 0, 0, 0, 0, 0, -12, -48, 0, 0, -60, 0, -18, 24, 0, 174, 0, 0, 0, 0, 0, -36, -78, 0, -36, 0, 0, 0, 42, 0, 18, -24, 0, 0, 0, 0, -60, -18, 0, 0, 48, 0, -18, 0, 0, 138, 0, 0, -36, 0, 0, 0, 84, 0, -72, 132, 0, 0, 6, 0, 0, -90, 0, -6, 72, 0, 6, 0, 0, -24, 60, 0, 24, 0, 0, 0, 0, 0, -24, 138, 0, 0, 24, 0, 36, -42, 0, -84, 0, 0, -24, 0, 0, -24, 108, 0, -48, 0, 0, 0, 24, 0, 0, -138, 0, 0, 6, 0, 42, 0, 0, 24, -42, 0, 36, 0, 0, 24, -60, 0, 144, 0, 0, 0, -12, 0, 18, -162, 0, 0, 0, 0, 48, -54, 0, 72, -120, 0, -6, 0, 0, -150, -6, 0, 0, 0, 0, 0, -24, 0, -42, 0, 0, 0, -60, 0, 42, 120, 0, -162, 108, 0, 0, 0, 0, 0, -102, 0, -12, 0, 0, 0, 0, 0, 12, 42, 0, 0, -192, 0, 0, 24, 0, -108, -96, 0, 0, 0, 0, -90, -42, 0, -18, 0, 0, 0, 60, 0, -42, -6, 0, 0, 156, 0, -42, 0, 0, 0, 90, 0, -54, 0, 0, -156, 0, 0, 24, 0, 0, 0, 126, 0, -36, -120, 0, 0, 42, 0, 0, 0, 0, 42, 60, 0, -30, 0, 0, -132, 48, 0, -24, 0, 0, 0, -240, 0, -150, -162, 0, 0, 120, 0, 12, -162, 0, 66, 0, 0, -84, 0, 0, 0, 138, 0, 0, 0, 0, 0, 30, 0, 0, 114, 0, 0, 138, 0, -48, 0, 0, -24, -60, 0, 12, 0, 0, 78, -216, 0, 72, 0, 0, 0, -96, 0, -18, 198, 0, 0, 0, 0, 168, -102, 0, -102, -120, 0, 30, 0, 0, 114, 24, 0, 0, 0, 0, 0, 18, 0, -48, 0, 0, 0, -72, 0, -96, -66, 0, 192, 144, 0, 78, 0, 0, 0, 0, 0, -42, 0, 0, 0, 0, 0, 180, -24, 0, 0, -192, 0, 42, -72, 0, 234, -30, 0, 0, 0, 0, 54, -12, 0, 36, 0, 0, 0, 126, 0, 60, 36, 0, 0, 12, 0, -120, 18, 0, 0, 180, 0, -54, 0, 0, -174, 0, 0, -132, 0, 0, 0, 180, 0, 66, 144, 0, 0, -114, 0, 0, 126, 0, -12, 24, 0, 12, 0, 0, 120, 42, 0, -12, 0, 0, 0, -84, 0, 114, 126, 0, 0, 144, 0, 0, 132, 0, -162, 0, 0, -36, 0, 0, 48, 210, 0, 60, 0, 0, 0, -36, 0, 0, -114, 0, 0, 84, 0, -18, 0, 0, -48, -78, 0, -12, 0, 0, -30, -132, 0, 180, 0, 0, 0, -72, 0, -42, 0, 0, 0, 0, 0, 24, 30, 0, 114, -180, 0, 90, 0, 0, 186, 36, 0, 0, 0, 0, 0, -180, 0, -48, 0, 0, 0, -102, 0, -42, -354, 0, -90, 204, 0, 156, 0, 0, 0, -54, 0, -48, 0, 0, 0, 0, 0, -12, 12, 0, 0, -156, 0, 132, 132, 0, -198, 12, 0, 0, 0, 0, 108, 30, 0, 18, 0, 0, 0, 72, 0, -6, -126, 0, 0, 204, 0, -42, 18, 0, 0, -48, 0, -24, 0, 0, 0, 0, 0, -48, 0, 0, 0, 210, 0, -30, -192, 0, 0, -48, 0, 0, 30, 0, -12, 0, 0, -24, 0, 0, 156, 102, 0, 12, 0, 0, 0, -96, 0, -48, -6, 0, 0, 144, 0, 18, 270, 0, 114, 0, 0, -120, 0, 0, -6, 198, 0, 24, 0, 0, 0, 126, 0, 0, 12, 0, 0, 48, 0, 72, 0, 0, 96, -60, 0, -12, 0, 0, -192, -12, 0, -12, 0, 0, 0, -48, 0, 42, -60, 0, 0, 0, 0, -24, 204, 0, -42, -234, 0, -6, 0, 0, 60, -72, 0, 0, 0, 0, 0, -102, 0, 162, 0, 0, 0, -120, 0, 96, 198, 0, 126, 0, 0, 78, 0, 0, 0, -162, 0, -102, 0, 0, 0, 0, 0, 0, -42, 0, 0, -132, 0, -210, 168, 0, 78, -36, 0, 0, 0, 0, -12, -186, 0, 0, 0, 0, 0, 36, 0, -102, 18, 0, 0, -12, 0, -72, -102, 0, 0, 36, 0, -18, 0, 0, 192, 0, 0, 0, 0, 0, 0, 60, 0, 84, 276, 0, 0, 54, 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, 4, -1, 6, 0], [1, 1, 8, 4, -1, 2, 0], [1, 1, 56, 13, 1, 6, 0]], "char_orbit_index": 37, "prim_orbit_index": 13, "minimal_twist": "56.2.m.a", "char_is_minimal": true, "conrey_index": 19, "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, 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, 0, -1, 0, 0, 0, 0, 0, 1, -1, 1], [-1, 1, 0, -1, -1, -1, -1, 1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 1, 1, 1, 0, -1, 0, 0, -1, 1], [3, -1, 1, 0, 2, 1, 2, -2, -1, -1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, -1, 0, 0, 1, 1, 0, -1, -1, -1], [0, -1, 0, -1, 0, 0, 0, -1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, -1, -2, -2, 0, 1, 1, 0, 2, -1], [0, 0, 0, -1, 3, 0, 1, -3, -1, 0, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 0, 0, -2, 0, 0, 2, 2], [0, 1, 0, -1, -1, 0, 0, 1, 1, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 0, -2, -2, 0, 0, 1, 2, 1, 0, 0], [2, 0, 1, -1, -1, 0, 0, 2, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, -1, 1, 1, 0, 0, 0, 1, 0, 0, 0], [1, -2, 2, 1, -1, 1, -1, -1, 0, -2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, -2, 0, 0, 0, 0, 2, 2, 0, 0], [-3, 0, -2, 1, -4, -1, -1, 3, 2, 0, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -3, 1, 0, 2, 2, 1, -1, 1, -2, 0, 2], [-1, 0, -2, -1, 0, 0, 0, 1, -1, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 3, -2, 0, 0, 1, -2, -2, -2, 1, 1], [0, 0, 0, 2, 0, 0, 0, 0, 0, -2, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, -1, -2, 0, -1, 0, 4, 0, 3, -1, 1], [-2, -1, 0, -3, -2, 0, 0, 0, 3, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, -4, 1, 2, 1, -1, 2, 0, 0, -4, 0], [4, -1, 0, 1, 2, 0, 2, 0, -1, 1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 0, 1, -2, -1, -1, -1, -2, 0, 0, 0], [-1, -2, 0, -1, 0, 0, 0, 1, 1, 2, 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], [-1, 2, -1, 1, 1, 1, -1, -1, 0, 1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 2, -1, 2, 0, -2, -1, 5, 0, -2, 0, -2], [0, 1, 2, -1, 0, -1, -1, 0, 0, 1, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, -1, 2, 0, 0, 1, 1, -2, 0, -1], [4, 0, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 0, 2, -2, 0, 0, 0, 0, 2, 0, -2], [-2, -3, -1, 3, -2, -2, -1, 2, 5, -3, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 1, 0, -1, -1, 1, 1, 0], [5, 1, 1, 4, 4, 1, 0, 2, -3, -1, -1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 2, 1, -2, 1, -1, 3, 0, 0, 2, -2], [-4, -2, 0, 2, 1, 0, 0, -3, -2, 2, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, -2, 3, -4, -3, -3, 4, 6, 0, 2, -2], [2, 0, 1, 1, -3, -2, 0, 6, 1, -4, 4, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -2, 2, 0, 4, 2, 4, -4, -2, -2, -2, 2], [1, -1, 0, 0, -1, 0, 0, 3, 0, 1, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 2, -1, 0, 0, -5, -2, -2, 0, 1], [4, 0, 1, 0, 1, 2, 2, -4, -4, -1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [7, -3, 0, 2, 4, 1, 3, 1, -1, 1, -3, 3], [-4, 2, -2, 0, -4, -2, -4, 4, 2, 2, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 0, 2, 0, 0, 0, 1, -2, 2, 0, 0], [4, -1, 2, 0, 6, 4, 2, -2, -3, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 2, 1, -1, 1, 0, -8, -1, -1, 3, 1], [-1, 0, -3, 3, 1, 2, -1, 1, 1, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 2, 3, -1, 3, -3, -1, 0, 0, 2, 0], [-4, 2, 2, -2, -2, 0, 2, -2, 2, -2, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 2, -4, -1, -2, -3, -3, 1, 2, 2, 4, -4], [-4, 4, 0, 2, 0, 0, 0, -6, -2, -4, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -3, -2, 2, 1, 2, 0, -3, -1, -1, -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], [2, -1, 1, -1, 4, 2, 1, -3, -1, 1, -5, 3], [-1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-7, -2, 0, 1, -2, 0, 0, -1, -1, 2, 0, 1], [-9, 1, -4, -3, -3, -1, -2, 4, -1, 1, 1, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -2, -3, 4, 0, 4, -2, -1, -3, -3, 1], [2, 1, 1, -1, -1, 2, 1, -2, -3, 1, 5, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 2, 0, 1, 0, 0, 0, 5, -1, -2, 0, -7], [1, 1, -4, -3, 0, -1, -3, 9, 0, 4, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 4, 0, 2, 0, 2, -2, -2, 0, 0, 0, 0]]}