# Stored data for newform 507.2.f.a, downloaded from the LMFDB on 19 January 2025.
{"Nk2": 2028, "analytic_conductor": 4.0484153824789155, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 39, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 6, "char_orbit_label": "f", "char_order": 4, "char_parity": 1, "char_values": [507, 4, [170, 340], [2, 3]], "cm_discs": [], "conrey_index": 239, "dim": 4, "field_disc": 256, "field_disc_factorization": [[2, 8]], "field_poly": [1, 0, 0, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 8, "has_non_self_twist": 1, "hecke_cutters": [[2, [1, 0, 0, 0, 1]], [5, [16, 0, 0, 0, 1]], [7, [2, 2, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 343630938619, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0], [1, 1, 13, 4, -1, 4, 0], [1, 1, 39, 6, 1, 4, 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": false, "label": "507.2.f.a", "level": 507, "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": false, "level_primes": [3, 13], "level_radical": 39, "minimal_twist": "39.2.f.a", "nf_label": "4.0.256.1", "prim_orbit_index": 6, "qexp_display": "q+\\zeta_{8}q^{2}+(-1-\\zeta_{8}-\\zeta_{8}^{3})q^{3}-\\zeta_{8}^{2}q^{4}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "507.2.f", "trace_display": [0, -4, 0, -4], "trace_hash": 1175757952860540585, "trace_moments": [{"__RealLiteral__": 0, "data": "0.009", "prec": 17}, {"__RealLiteral__": 0, "data": "3.974", "prec": 17}, {"__RealLiteral__": 0, "data": "0.672", "prec": 17}, {"__RealLiteral__": 0, "data": "94.233", "prec": 20}, {"__RealLiteral__": 0, "data": "23.772", "prec": 20}, {"__RealLiteral__": 0, "data": "3049.811", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.626", "prec": 17}, "traces": [0, 4, 0, -4, 0, 0, 4, -4, 0, -4, 0, 0, 0, 0, 0, -8, 4, 0, -8, -4, 0, 4, -16, 0, -12, 0, 0, 20, -4, 0, 0, 20, 0, 16, 0, 0, 0, -4, 0, 0, -24, 0, -8, 0, 0, 16, -24, 0, -4, 0, 0, 0, 0, 0, 4, 32, 0, 4, -8, 0, 8, 32, 0, 4, 0, 0, 16, 20, 0, 0, -8, 0, 24, -4, 0, 0, 4, 0, 0, -40, 0, -28, 0, 0, 4, 0, 0, 16, 0, 0, 0, 0, 0, -20, -16, 0, -20, -28, 0, -32, -4, 0, 0, 0, 0, 16, 16, 0, 0, -4, 0, 4, -4, 0, 0, 48, 0, 0, -16, 0, 24, 0, 0, -8, -20, 0, 16, 0, 0, 0, 0, 0, 16, 8, 0, -8, 0, 0, 24, -16, 0, 16, 0, 0, -4, 16, 0, 0, -4, 0, -4, -4, 0, 0, 16, 0, 0, 56, 0, -32, 0, 0, 16, -4, 0, -32, 0, 0, 0, 0, 0, 4, -24, 0, 8, -4, 0, 16, 56, 0, -16, 0, 0, -32, -72, 0, 0, 0, 0, -20, 8, 0, 0, -76, 0, 0, -20, 0, 16, 0, 0, -20, 24, 0, 0, 0, 0, 0, 0, 0, 8, 56, 0, 16, 16, 0, -12, -40, 0, 4, 0, 0, -8, 44, 0, 0, 40, 0, -4, -4, 0, 0, 24, 0, 0, 32, 0, 40, 0, 0, -8, 68, 0, -4, 0, 0, 0, 0, 0, -32, -48, 0, 4, 96, 0, 0, -68, 0, -24, 0, 0, -32, -32, 0, 0, -32, 0, -56, -20, 0, 0, -76, 0, 0, 56, 0, 48, 0, 0, -20, 24, 0, 16, 0, 0, 0, 0, 0, 40, -68, 0, 28, -4, 0, -20, 32, 0, 16, 0, 0, 4, -24, 0, 0, -4, 0, 0, 68, 0, 0, -40, 0, 0, 32, 0, -32, 0, 0, -16, -32, 0, -32, 0, 0, 0, 0, 0, 4, -24, 0, 32, -28, 0, 4, -16, 0, 4, 0, 0, -80, 0, 0, 0, -48, 0, -48, 24, 0, 0, 68, 0, 0, 80, 0, 16, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 32, 32, 0, 16, -8, 0, 20, -16, 0, 48, 0, 0, -8, -76, 0, 0, -8, 0, 12, -32, 0, 0, 28, 0, 0, 0, 0, 64, 0, 0, -32, 68, 0, -8, 0, 0, 0, 0, 0, -32, 16, 0, 0, 92, 0, -56, 24, 0, 24, 0, 0, 16, 16, 0, 0, -100, 0, -32, -48, 0, 0, -32, 0, 0, -48, 0, 20, 0, 0, -16, 4, 0, -8, 0, 0, 0, 0, 0, 4, -112, 0, -8, -28, 0, 8, 32, 0, 4, 0, 0, 24, 116, 0, 0, 48, 0, -16, 68, 0, 0, 72, 0, 0, -40, 0, -56, 0, 0, -40, 4, 0, 64, 0, 0, 0, 0, 0, 48, -20, 0, -44, -76, 0, 4, -40, 0, 8, 0, 0, -32, 20, 0, 0, 92, 0, 16, -72, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, -20, -24, 0, 24, 0, 0, 0, 0, 0, 8, 80, 0, 4, 64, 0, 16, 196, 0, -32, 0, 0, -56, -32, 0, 0, -56, 0, 8, -4, 0, 0, 0, 0, 0, -112, 0, -32, 0, 0, 72, 40, 0, 16, 0, 0, 0, 0, 0, 0, 56, 0, 16, -80, 0, 28, 48, 0, -8, 0, 0, 16, -8, 0, 0, -4, 0, 76, -16, 0, 0, 64, 0, 0, 56, 0, 20, 0, 0, 88, -4, 0, -80, 0, 0, 0, 0, 0, -12, 32, 0, -20, -4, 0, -24, -160, 0, -16, 0, 0, 0, -4, 0, 0, 48, 0, 24, -4, 0, 0, -24, 0, 0, 76, 0, -32, 0, 0, 8, -76, 0, -56, 0, 0, 0, 0, 0, -32, 24, 0, -16, 20, 0, 48, 0, 0, -48, 0, 0, 40, -4, 0, 0, 64, 0, 4, 16, 0, 0, -4, 0, 0, -96, 0, 16, 0, 0, -44, -40, 0, 40, 0, 0, 0, 0, 0, -40, 56, 0, -32, -80, 0, -4, -112, 0, 4, 0, 0, 96, 44, 0, 0, 40, 0, -24, 0, 0, 0, 4, 0, 0, 8, 0, -32, 0, 0, 16, -76, 0, 40, 0, 0, 0, 0, 0, -80, -16, 0, 16, 24, 0, -68, 0, 0, -20, 0, 0, 92, -8, 0, 0, 20, 0, 40, 120, 0, 0, -4, 0, 0, -32, 0, -120, 0, 0, 64, 0, 0, 48, 0, 0, 0, 0, 0, -20, -64, 0, -96, 24, 0, 0, 8, 0, 0, 0, 0, 68, -52, 0, 0, -76, 0, 48, -20, 0, 0, -48, 0, 0, -64, 0, 16, 0, 0, 32, -76, 0, -128, 0, 0, 0, 0, 0, 32, 0, 0, 8, 0, 0, 112, -88, 0, 20, 0, 0, 112, 72, 0, 0, -4, 0, 76, 16, 0, 0, 24, 0, 0, 16, 0, -56, 0, 0, 16, 16, 0, -96, 0, 0, 0, 0, 0, -16, 32, 0, 100, -32, 0, -24, 84, 0, -56, 0, 0, 16, -20, 0, 0, 0, 0, -16, -148, 0, 0, -48, 0, 0, 56, 0, 16, 0, 0, -20, -48, 0, 68, 0, 0, 0, 0, 0, 28, 48, 0, 4, -52, 0, -56, 32, 0, 40, 0, 0, -32, -80, 0, 0, 0, 0, 64, -44, 0, 0, 0, 0, 0, -88, 0, 4, 0, 0, 24, -120, 0, -8, 0, 0, 0, 0, 0, 4, 128, 0, -64, -4, 0, 0, -136, 0, -68, 0, 0, -32, -4, 0, 0, 40, 0, 40, 20, 0, 0, 72, 0, 0, -208, 0, -32, 0, 0, 56, 48, 0, 16, 0, 0, 0, 0, 0, 40, 0, 0, -16, 16, 0, 32, 128, 0, 56, 0, 0, 64, 68, 0, 0, 92, 0, 0, 56, 0, 0, 16, 0, 0, 32, 0, -8, 0, 0, 4, 120, 0, 24, 0, 0, 0, 0, 0, -64, -64, 0, 28, 16, 0, 32, 104, 0, -20, 0], "weight": 2, "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, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [-1, -1, 0, -1], [0, 0, -1, 0], [0, -2, 0, 0], [1, -1, -1, 0], [-1, 0, -1, 0], [0, 0, 0, -3], [-1, 2, 0, 2], [0, 0, -2, 0], [0, 0, 0, 4], [0, -1, 1, 1], [0, 0, 0, 0], [0, -1, 0, -1], [-2, 2, 2, 0], [1, 0, 0, 0], [0, 0, 0, 0], [-2, -1, 2, 0], [-1, 0, 1, 0], [0, 0, 0, 2], [1, 0, 1, 2], [-4, 0, 0, 0], [0, -6, 0, 6], [-3, 0, -3, 3], [0, 0, -1, 0], [0, 0, 0, 0], [5, -1, 0, -1], [-1, 0, 1, 0], [0, 2, 0, 2], [0, -2, 2, 2], [5, 0, -5, 0], [0, -5, 0, 0], [4, 0, 4, -4], [0, 0, 0, 0], [0, 2, 0, 2], [0, 2, 1, -2], [-1, 0, -1, 0], [0, -1, 0, 1], [0, 0, 0, 0], [-6, 0, 0, 0], [0, -2, 0, 0], [-2, 1, 0, 1], [0, 0, -6, 0], [0, 4, 0, 0], [4, 2, -4, 0], [-6, 0, -6, 0], [0, 0, 0, 4], [-1, -1, 0, -1], [0, 0, -5, 0], [0, 0, 0, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, -4, 0, -4], [1, 5, -1, 0], [8, 0, 0, 0], [0, -3, 0, 3], [1, 2, -1, 0], [-2, 0, 2, 0], [0, 0, 0, 4], [2, 0, 2, -2], [8, 0, 0, 0], [0, 5, 0, -5], [1, 0, 1, -4], [0, 0, -7, 0], [0, 0, 0, 0], [4, 4, 0, 4], [5, 0, -5, 0], [0, 0, 0, 0], [0, 6, 12, -6], [-2, 0, 2, 0], [0, 4, 0, 0], [6, 0, 6, 3], [-1, 0, -1, 0], [0, -1, 0, -1], [0, -1, 1, 1], [1, 0, 1, 0], [0, 4, 0, -4], [0, 0, 0, 0], [-10, 0, 0, 0], [0, -2, 0, 0], [-7, -4, 0, -4], [0, 0, -2, 0], [0, -8, 0, 0], [1, 2, -1, 0], [0, 0, 0, 0], [0, 0, 0, -6], [4, -2, 0, -2], [0, 0, 12, 0], [0, 0, 0, -14], [0, 4, 2, -4], [0, 0, 0, 0], [0, 6, 0, 6], [-5, -10, 5, 0], [-4, 0, 0, 0], [0, 2, 0, -2], [-5, 5, 5, 0], [-7, 0, 7, 0], [0, 0, 0, -5], [-8, 0, -8, -4], [-1, 0, 0, 0]]}