# Stored data for newform 475.2.a.g, downloaded from the LMFDB on 24 April 2024.
{"label": "475.2.a.g", "space_label": "475.2.a", "level": 475, "weight": 2, "hecke_orbit": 7, "hecke_orbit_code": 27021597797777883, "dim": 3, "is_polredabs": true, "nf_label": "3.3.169.1", "trace_hash": 2148923321021157602, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [5, -3, -2, 1]]], "qexp_display": "q+(1-\\beta _{1})q^{2}+(1+\\beta _{2})q^{3}+(2-\\beta _{1}+\\cdots)q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1900, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 3.7928940960108184, "hecke_ring_index": 1, "level_radical": 95, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.006", "prec": 17}, "analytic_rank_proved": true, "char_values": [475, 1, [77, 401], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [5, 19], "conrey_indexes": [1], "field_disc": 169, "field_disc_factorization": [[13, 2]], "field_poly": [-1, -4, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.033", "prec": 17}, {"__RealLiteral__": 0, "data": "2.847", "prec": 17}, {"__RealLiteral__": 0, "data": "0.684", "prec": 17}, {"__RealLiteral__": 0, "data": "22.080", "prec": 20}, {"__RealLiteral__": 0, "data": "12.338", "prec": 20}, {"__RealLiteral__": 0, "data": "258.191", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[5, 1], [19, -1]], "trace_display": [2, 2, 0, 4], "traces": [0, 3, 2, 2, 4, 0, -3, 4, 3, 1, 0, 1, 7, 3, 7, 0, -6, 14, -8, 3, 0, -6, 5, 8, 15, 0, -11, -1, 1, -5, 0, -1, 3, -8, 5, 0, -3, 5, 2, -11, 0, 1, -4, -5, -3, 0, -12, 9, -4, -7, 0, 18, -22, 31, -5, 0, -9, 2, 1, -6, 0, 3, -5, -3, 1, 0, -1, -13, 23, 1, 0, 7, 1, 1, -1, 0, 4, 10, -42, -18, 0, -21, -34, 3, 5, 0, 40, -12, -12, -20, 0, 17, -11, 21, 45, 0, 2, -13, 4, -4, 0, 12, -14, -16, -36, 0, 12, -4, -23, 5, 0, 38, -8, -14, -3, 0, -11, 14, -30, 10, 0, -24, -11, 5, 16, 0, -2, -30, -27, -12, 0, 5, -2, 4, -39, 0, 27, 37, -47, -7, 0, -7, 22, 14, -15, 0, 18, -35, 37, -9, 0, -4, 3, 9, 11, 0, -19, 4, 1, 12, 0, 15, -1, 49, -29, 0, -50, -13, 20, 42, 0, 1, 28, 0, 5, 0, -2, 22, -48, -3, 0, 1, 20, 15, -18, 0, 14, -4, 38, 16, 0, 21, -21, 19, 13, 0, -31, 29, 6, -33, 0, 0, 47, 2, 37, 0, 11, 20, -45, 1, 0, -19, 24, -4, 58, 0, -40, -23, 64, 5, 0, 1, 21, -45, 4, 0, 21, -45, 7, 0, 0, -15, -18, -11, 5, 0, -8, 14, 24, -21, 0, -45, -16, -11, 4, 0, -66, 3, 38, 67, 0, -18, -4, 7, -46, 0, -20, 32, 83, -28, 0, -6, 38, 7, 5, 0, 7, -9, -39, 26, 0, 5, -28, -45, 42, 0, -3, 27, 4, 4, 0, 2, 56, -25, 18, 0, 31, -3, 14, 23, 0, -39, 23, 28, -6, 0, 70, 17, 20, 73, 0, 2, -33, -44, -6, 0, -46, -22, -4, -2, 0, -7, 15, -15, -58, 0, 15, 61, -57, 7, 0, -7, 23, 14, -15, 0, 37, -53, -25, 25, 0, 10, 17, 6, -78, 0, 25, 7, 93, -31, 0, -22, -8, -7, 21, 0, 13, -7, -16, 4, 0, 64, 1, 22, -20, 0, -57, -15, 50, -43, 0, 3, 44, -29, -25, 0, -16, 19, -55, 35, 0, 50, 15, 29, 19, 0, 22, 8, 15, -21, 0, -7, -25, -47, -70, 0, 108, -45, -26, -25, 0, 33, -59, -27, 41, 0, -1, -22, -61, -6, 0, -28, -39, -53, 3, 0, -3, -33, 70, 42, 0, 3, 9, -34, -17, 0, 42, -74, 5, -26, 0, -5, -4, -36, 5, 0, 19, -9, 51, -34, 0, -57, -24, -8, -24, 0, 11, 8, 38, -5, 0, -11, -86, 19, 42, 0, -4, 33, 23, 35, 0, -4, -10, -7, -56, 0, 15, -37, -65, -22, 0, -40, -23, -20, 10, 0, -29, 23, 36, -26, 0, 59, 20, 7, 70, 0, 9, 19, 51, 64, 0, -86, -82, -42, -45, 0, 62, -25, 16, 11, 0, -21, -28, -32, -11, 0, 15, 18, -42, -36, 0, 13, 27, -34, -3, 0, 35, -24, -53, -41, 0, -3, -46, -1, -35, 0, 23, 16, -23, 52, 0, 4, 22, 18, 11, 0, -17, 17, 29, 13, 0, 24, 1, 92, -45, 0, -26, -54, 13, 28, 0, 65, -53, 44, 14, 0, -56, -52, 45, 14, 0, -5, 40, -50, -34, 0, -70, 88, -19, -109, 0, -33, 62, -53, 47, 0, 18, -28, 7, -12, 0, 17, -3, 92, -2, 0, 22, 18, -28, -61, 0, -61, 26, 19, 27, 0, 36, 41, -38, -1, 0, -24, 16, 9, 20, 0, 53, -22, 66, 11, 0, 7, -3, 26, -40, 0, 14, -39, 3, -3, 0, -69, -14, -56, -6, 0, -29, 24, 68, 19, 0, 45, 17, -31, -17, 0, -49, -8, 1, 58, 0, 5, 47, -30, 32, 0, 55, 58, -4, -15, 0, -87, 121, 54, -19, 0, 5, 0, -8, -28, 0, 41, 48, 56, 60, 0, -67, -17, 34, 14, 0, 54, -15, -21, 81, 0, -48, -9, -65, -4, 0, -12, -19, -62, 87, 0, 69, -11, 53, 13, 0, -17, -19, -38, -3, 0, -35, 65, 88, 83, 0, -58, 65, -1, -35, 0, -25, 9, -97, -42, 0, 58, 125, 5, 22, 0, -7, 68, -14, -7, 0, -19, -46, -33, 3, 0, -4, 25, -7, 65, 0, -30, 2, -17, 88, 0, 11, -14, -87, 34, 0, -32, 7, 35, -74, 0, 47, -13, -7, -10, 0, -11, 81, 36, -5, 0, -37, 53, -14, -1, 0, -6, 47, 1, 53, 0, -22, 14, -53, -43, 0, 21, -9, 63, 67, 0, 25, -6, 17, 44, 0, 82, 47, 74, 22, 0, -52, 55, 70, 1, 0, 11, -95, 19, 1, 0, 34, -25, 17, -17, 0, 3, -4, 3, 7, 0, -83, -55, -4, 29, 0, 28, -127, -4, -52, 0, -109, -13, -53, 61, 0, 52, -6, 90, -22, 0, -49, -5, 54, -3, 0, 43, -24, -2, 23, 0, -40, -26, 31, 48, 0, 70, 131, -63, -45, 0, -3, -56, -91, 1, 0, -70, -129, 36, -34, 0, -11, -19, -88, -73, 0, -43, 25, 101, -6, 0, 48, -20, -14, 1, 0, -28, 1, 29, 25, 0, -14, 89, 17, -32, 0, 52, -47, -26, -12, 0, 24, 8, -25, -55, 0, 38, 49, 60, -107, 0, 4, -26, 25, -53, 0, -7, -8, 9, 100, 0, 16, 14, 45, -20, 0, 136, 32, 36, -27, 0, -61, 18, -73, -35, 0, 9, -4, -64, -3, 0, 0, 37, -45, 26, 0, 7, 47, -19, 6, 0, -35, -27, -5, 3, 0, -7, -71, 69, -28, 0, 53, -14, -39, 16, 0, 53, -69, 98, -14, 0, -43, -38, -3, -64, 0, 45, -16, 11, -74, 0, 76, 9, 34, 71, 0, -32, -209, -62, -99, 0, -41, 116, -50, 18, 0, -54, 33, 60, 44, 0, -19, 3, -62, -11, 0, -59, -14, -49, 5, 0, 9, -5, -22, -126, 0, -35, -14, -41, 25, 0, 20, -68, -89, -97, 0], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "475.2.a.e", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0], [1, 0, 0], [1, -1, 0], [1, 0, 1], [2, -1, 1], [0, 0, 0], [0, -2, 1], [1, 0, -1], [2, -1, 2], [0, 1, 0], [0, 0, 0], [0, 0, -1], [3, -1, 1], [-1, 3, -3], [2, 0, -1], [0, 0, 0], [-1, -2, 1], [5, 0, 1], [-3, 0, -1], [1, 0, 0], [0, 0, 0], [-1, -1, 2], [1, 1, -1], [1, 3, -2], [5, 0, 0], [0, 0, 0], [-7, 4, -6], [-2, 2, -3], [1, -1, 1], [-2, 0, -1], [0, 0, 0], [1, -1, 3], [0, 2, -1], [-2, -1, 1], [4, -6, 1], [0, 0, 0], [-2, 2, -1], [4, -2, 5], [1, -1, 0], [-4, 3, 2], [0, 0, 0], [-2, 5, -2], [0, -1, 3], [1, -6, 2], [-1, 0, 0], [0, 0, 0], [-6, 1, -5], [5, -5, 1], [-1, -3, -2], [-4, 1, -4], [0, 0, 0], [7, 1, 4], [-11, 7, -4], [9, 2, -2], [-5, 5, -5], [0, 0, 0], [-1, -2, 4], [1, 0, 1], [-1, 3, -1], [-2, 2, 2], [0, 0, 0], [1, 1, 1], [1, -4, 4], [-1, 0, 0], [-3, 5, -5], [0, 0, 0], [0, 1, 2], [-6, 4, -1], [11, -5, 5], [0, 4, 3], [0, 0, 0], [3, -2, 0], [-1, 3, -1], [2, -3, 2], [5, -9, 7], [0, 0, 0], [2, -1, 1], [2, 1, -3], [-15, 2, -1], [-3, -4, 5], [0, 0, 0], [-6, -2, 1], [-15, 4, -7], [2, 3, 6], [2, -1, 0], [0, 0, 0], [17, -3, 8], [-4, -1, -1], [-3, -1, 2], [-9, 5, -2], [0, 0, 0], [2, 3, -8], [-6, 5, -2], [6, 1, -2], [19, -6, 6], [0, 0, 0], [0, 3, 1], [-5, -1, -3], [-3, 8, -5], [-1, -1, 0], [0, 0, 0]]}