# Stored data for newform 403.2.be.b, downloaded from the LMFDB on 19 April 2024.
{"label": "403.2.be.b", "space_label": "403.2.be", "level": 403, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4505661245227411, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 624526582964140632, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [1, -2, 2, 2, 1]], [7, [169, -130, 41, -8, 1]]], "qexp_display": "q+(-\\zeta_{12}-\\zeta_{12}^{2})q^{2}+(1-\\zeta_{12}+\\zeta_{12}^{2}+\\cdots)q^{3}+\\cdots", "char_order": 12, "char_parity": 1, "char_degree": 4, "char_conductor": 403, "char_orbit_label": "be", "char_is_real": false, "Nk2": 1612, "analytic_conductor": 3.2179712014575994, "hecke_ring_index": 1, "level_radical": 403, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 12, "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": "0.098", "prec": 17}, "analytic_rank_proved": true, "char_values": [403, 12, [249, 313], [9, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [13, 31], "conrey_indexes": [57, 99, 161, 398], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.907", "prec": 17}, {"__RealLiteral__": 0, "data": "0.162", "prec": 17}, {"__RealLiteral__": 0, "data": "45.354", "prec": 20}, {"__RealLiteral__": 0, "data": "16.019", "prec": 20}, {"__RealLiteral__": 0, "data": "837.392", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c12", "trace_display": [-2, 6, -2, 8], "traces": [0, 4, -2, 6, 0, -2, 2, 8, 2, 2, -6, 0, -6, -4, 10, -4, 4, 0, 2, 12, 6, 14, -12, 4, 2, 0, -16, 0, -12, 0, -8, 14, -18, 0, 0, 4, -6, -12, -30, -12, -2, 16, 18, -2, 12, -10, 16, 20, -6, -18, -6, 0, 12, -30, -8, -6, 6, 18, 2, 2, 12, 0, -22, 34, 0, 2, -12, -22, 0, 24, -20, -2, -2, 18, 12, -6, 24, 24, -20, -36, 10, -2, -24, 34, -18, 0, 22, -22, 0, 16, 6, 10, 0, 36, -44, 0, -30, -20, 46, -18, 0, 0, 0, 18, -8, -12, 38, 6, 0, -12, 6, 0, -4, 0, -18, -20, -24, -32, 22, 0, 0, -18, -22, 32, 30, 32, -28, 8, -22, 12, 6, 0, 12, 18, -6, -8, 0, 0, 20, 0, 0, 20, 30, -12, -22, 2, 30, -8, 12, -4, -6, -38, 6, 0, -42, -22, 24, -16, -4, -52, -6, 26, 16, -14, 24, 0, -34, -4, 14, 10, 0, 6, -6, -48, 2, -24, 12, -16, 0, -18, 18, 38, -40, 14, 20, 0, -8, 0, 24, 40, -24, -6, 2, 18, 0, 16, -18, 2, 24, -8, -6, -44, 30, 26, 0, -36, 10, 38, 32, 0, -16, 10, -30, -4, 18, 4, -8, 58, 0, 36, 6, 0, 0, 24, 18, 0, 0, -22, 42, 46, 12, 6, -22, 0, 10, -20, -42, -40, 0, 4, 20, -42, -10, 6, 36, 4, -8, 18, 22, 76, -32, 8, -6, -18, -52, 0, 36, 36, 20, -36, 6, -72, -60, 0, 0, 26, 18, 20, 6, -72, 8, 12, 0, -38, -24, 18, -24, -64, 56, 22, -16, -44, -24, 0, -30, -12, 6, 112, -54, 34, -2, -64, -30, -60, 28, 40, 12, -24, 36, -58, 18, -46, 0, -18, 72, -22, 0, 38, 0, 64, -6, 0, -8, -60, 38, -34, 36, -24, 8, -6, 14, 48, -26, 0, -6, 36, 56, -72, 16, 102, 0, -8, 42, 48, 18, 30, -46, 52, 4, 0, 0, -30, 0, -54, 14, -40, 16, 6, -66, -32, 36, -24, -36, -46, 24, 18, -12, 0, 78, -34, 14, 54, 38, -28, -18, -12, -22, 48, -68, -28, 24, -94, 24, 80, 0, 32, 0, -6, -48, 18, 12, -12, -6, 30, -22, 18, 30, 68, -24, 10, 8, 0, 10, -60, -2, 8, 6, -30, -8, 0, 36, 44, -28, -44, -48, 4, 0, 0, 0, -78, 4, 0, 18, -102, 38, -4, -24, -64, -66, 120, 12, -34, -26, -62, -22, 0, 28, 56, 18, 6, 0, -38, 0, 48, -40, 44, -48, -78, 48, -12, 6, 66, 0, 32, 48, 12, 54, -32, -52, 4, -30, -60, 0, -58, -18, 50, 42, -48, -78, 0, -12, -20, -18, -8, 0, -44, 24, 0, 48, -76, -20, 6, -18, 24, -40, 36, 0, -6, -4, 28, 24, 0, 78, 104, 18, 24, 62, 46, 14, -14, 32, 2, -24, 0, -72, 0, 14, -68, 0, -8, 0, -14, 68, -8, 0, 30, 42, 54, 24, -2, 0, 12, -10, 24, -48, -32, 12, -42, -36, -128, 14, -36, 4, 0, 0, -48, 84, 0, 24, 20, 34, 28, -54, -88, 16, -12, -22, -12, 84, 18, 24, 60, 0, 0, 0, 48, -30, 12, 24, -6, -36, 78, 20, -52, -4, -24, -120, 12, 52, 8, 76, 0, -28, -18, -12, 24, -52, -34, -2, -56, -24, -14, 24, 0, -92, -54, 42, 46, 34, 24, 42, 0, -20, 30, 18, 4, -36, 50, 0, -18, -44, 20, -36, 24, 24, 0, -60, 0, 38, -54, 6, 72, 46, -20, 18, 20, 30, 18, -54, -26, 22, -38, 0, 40, -14, -32, -18, 56, 28, -2, 6, 0, -64, -26, 60, -2, -10, 6, 0, 0, -34, 70, -4, 24, 72, -16, 0, -6, 6, 44, 22, 54, 24, 44, 78, -28, 0, 180, 8, 84, -30, 94, -42, 48, -12, 0, -8, 54, -46, -52, 0, 40, 8, 0, 42, 102, 0, 0, -24, 18, 14, -48, -30, -40, -26, 24, 30, 18, 0, -26, 0, -44, -12, 26, 102, -12, 0, 32, -38, 48, -8, -12, -48, -48, 34, 56, -86, 0, -52, -24, -36, 0, 8, -108, 36, 0, -14, -78, -24, -24, -14, 0, 4, 14, 0, -36, -54, 28, 34, -32, -22, 40, -146, -36, -114, 30, -28, -36, -48, 92, -24, 0, 42, -38, -24, -20, 0, 24, 96, 66, -48, -6, 0, 76, 52, 0, 14, 122, 0, -30, 0, -108, 68, 108, -14, -18, -24, 36, -36, -36, -12, -56, -44, -66, 18, 0, -30, 100, 18, 90, -66, 60, -42, -64, -28, 0, -44, 0, 16, 0, -24, 48, 0, -80, -102, -22, -60, 2, 18, -72, 64, -72, 12, -48, -18, 44, 24, 34, 36, 0, 18, 38, 0, 18, 72, -104, -26, -132, -18, 12, 0, 84, -78, 48, 48, 14, 0, -66, -42, -88, 36, -24, -24, 8, 46, 18, 194, 6, -114, -8, -64, -132, 36, 0, 56, 0, 72, 0, -60, -50, -16, -32, 42, -44, 30, -68, 62, -58, -54, 32, 0, 24, -24, -84, -114, -102, 42, 36, -6, 18, -36, 132, 0, -34, -72, 64, -18, 0, 18, -24, 0, 82, -60, -106, 78, 144, -84, 22, 28, -144, -42, 20, -22, -100, 0, 36, 32, -30, 48, 112, -44, 18, -84, 102, 32, 36, -90, -120, 0, 60, 72, 0, 24, 20, 0, 38, -38, 0, 18, 12, -70, 0, 30, 30, 48, -28, 18, 120, 0, 50, -20, 128, 56, 38, -6, -36, 0, 102, -78, -12, -28, -144, -48, -16, 20, 0, 26, 2, -10, -70, 60, 74, 22, 52, 38, 0, 0, 56, 120, -42, -36, -48, 0, -96, -56, -36, 24, 24, 62, 48, -4, -26, 72, 132, -30, 24, 0, 36, -10, 0, 16, -20, 6, -100, -46, 42, 0, 52, 42, 42, -60, -114, 2, -48, 0, -8, 0, 56, 30, 52, 36, 0, -78, 52, 106, -68, 84, 20, 62, 48, 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": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 403, 31, 1, 12, 0]], "char_orbit_index": 31, "prim_orbit_index": 31, "minimal_twist": "403.2.be.a", "char_is_minimal": true, "conrey_index": 57, "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, -1, 0], [1, -1, 1, 0], [-1, 0, 2, 0], [0, 1, -1, -1], [1, -1, -1, 0], [1, -1, 2, 3], [0, -1, 1, 0], [0, -2, 1, -2], [-2, -1, 1, 1], [1, 1, -2, -2], [-3, 1, 3, -2], [0, 3, -2, -3], [5, 2, -5, -4], [0, 2, -2, 0], [1, 4, 0, -2], [0, 0, 0, 0], [-1, -2, 3, 3], [5, 5, -4, -1], [2, 1, -1, 1], [2, -5, 3, 3], [-4, -3, 2, 3], [1, -6, 0, 3], [-1, -1, 3, -2], [0, 3, 0, 0], [-5, -3, 2, 2], [0, 0, 0, -4], [-5, -5, 4, 1], [-2, 0, 4, -5], [-2, 0, 0, 0], [6, 0, -5, 0], [-4, -1, -1, -4], [1, 2, -2, -1], [0, 0, 0, 0], [1, 6, 0, -3], [-2, 6, 1, -6], [-2, -2, -2, 4], [-5, -6, -5, 0], [-1, 6, -4, -1], [0, 1, -1, 1], [6, -2, -4, -4], [6, 1, -3, -1], [-1, -3, 1, 6], [3, 3, 0, 0], [-1, -1, -3, 4], [3, 2, 2, 3], [7, 4, -4, -7], [-1, 5, -1, 0], [-6, -7, 3, 7], [0, 0, -3, -3], [0, 0, 0, 0], [4, 3, -2, 3], [-10, -2, 5, 2], [-4, -4, 4, 4], [-1, -3, -1, 0], [1, -4, 1, 0], [8, 1, -7, 7], [-1, -3, 3, 1], [-3, 3, 7, 4], [4, -2, -2, 4], [3, 0, -6, -2], [-5, -6, -1, 5], [8, -1, 1, -8], [-1, 0, 2, 4], [1, -5, -1, 0], [-3, -2, 0, 1], [-5, 6, -1, -1], [0, 0, 0, 0], [4, -10, 4, 0], [-3, -4, -4, -3], [-3, -2, 5, 5], [-3, 2, 5, -5], [2, -7, 5, 5], [2, 6, 2, 0], [0, 3, -3, 3], [3, -3, 6, 9], [6, 10, 0, -5], [-5, 0, 0, -1], [-6, 2, -6, 0], [4, -1, -3, -3], [-1, -2, 1, 4], [-8, -10, 4, 10], [12, 5, -7, 7], [-8, -1, 7, -7], [0, 0, 0, 0], [7, 7, -3, -4], [-11, 7, 11, -14], [0, 1, 0, 1], [3, 2, 2, 3], [1, 5, 1, 0], [1, 15, 3, -7], [-1, 0, 2, -9], [11, -6, -4, 5], [-11, -14, 0, 7], [1, 0, -2, -9], [-7, 7, -1, -8], [-7, 4, 4, -7], [10, 13, 3, -3], [-4, -4, -1, 5], [0, -3, 0, 6]]}