# Stored data for newform 1600.1.bd.a, downloaded from the LMFDB on 19 April 2024.
{"label": "1600.1.bd.a", "space_label": "1600.1.bd", "level": 1600, "weight": 1, "hecke_orbit": 1, "hecke_orbit_code": 1992881604160, "dim": 8, "is_polredabs": true, "nf_label": "8.0.4000000.1", "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [1, 2, 4, 3, 1]]], "qexp_display": "q+(-1+\\zeta_{20}^{6})q^{3}-\\zeta_{20}^{3}q^{5}+\\zeta_{20}^{5}q^{7}+\\cdots", "char_order": 10, "char_parity": -1, "char_degree": 4, "char_conductor": 200, "char_orbit_label": "bd", "char_is_real": false, "Nk2": 1600, "analytic_conductor": 0.7985040202128039, "hecke_ring_index": 1, "level_radical": 10, "projective_image": "A5", "projective_image_type": "A5", "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 20, "field_poly_is_real_cyclotomic": false, "projective_field_label": "5.1.25000000.3", "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [1600, 10, [1151, 901, 577], [5, 5, 4]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [2, 5], "conrey_indexes": [31, 671, 991, 1311], "field_disc": 4000000, "field_disc_factorization": [[2, 8], [5, 6]], "field_poly": [1, 0, -1, 0, 1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "trace_display": [0, -6, 0, 0], "traces": [0, 8, 0, -6, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, -6, 0, -4, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, -2, 0, 8, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -6, 0, 2, 0, 0, 0, 0, 0, -6, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, -2, 0, 6, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -6, 0, -4, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, -6, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, -8, 0, 0, 0, 0, 0, 4, 0, 8, 0, 0, 0, 0, 0, 4, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 8, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 2, 0, 8, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 6, 0, -2, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 4, 0, -6, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 6, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, -6, 0, 0, 0, 0, 0, -2, 0, -6, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 6, 0, -2, 0, 0, 0, 0, 0, 6, 0, -6, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -6, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, -4, 0, 6, 0, 0, 0, 0, 0, -6, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 6, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 8, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 12, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -6, 0, 2, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -8, 0, 6, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -6, 0, 6, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, -2, 0, -8, 0, 0, 0, 0, 0, -4, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, -4, 0, 8, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -6, 0, -6, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, -6, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -4, 0, -12, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -6, 0, -2, 0, 0, 0, 0, 0, -8, 0, -6, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 6, 0, -4, 0, 0, 0, 0, 0, -6, 0, 4, 0, 0, 0, 0, 0, -6, 0, 6, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, -4, 0, -6, 0, 0, 0, 0, 0, 6, 0, 6, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 4, 0, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 6, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, -2, 0, -8, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 6, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, -2, 0, -8, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 6, 0, 0, 0, 0, 0, -6, 0, -6, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 0, 6, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, 0, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -2, 0, -6, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -8, 0, 2, 0, 0, 0, 0, 0, 6, 0, -2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 4, 0, 6, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -6, 0, 8, 0, 0, 0, 0, 0, 6, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, -12, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, -6, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0], "projective_field": [-32, 60, -40, 10, 0, 1], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 4, -1, 2, 0], [1, 1, 25, 4, 1, 5, 0], [1, 1, 200, 14, -1, 10, 0]], "char_orbit_index": 30, "prim_orbit_index": 14, "minimal_twist": "1600.1.bd.a", "char_is_minimal": true, "conrey_index": 31, "id": null, "trace_hash": null, "fricke_eigenval": null, "atkin_lehner_string": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "trace_zratio": null, "trace_moments": null, "sato_tate_group": null, "atkin_lehner_eigenvals": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[], [[1, 0]], [], [[-1, 0], [1, 6]], [], [[-1, 3]], [], [[1, 5]], [], [[1, 0], [-1, 2], [-1, 6]], [], [[-1, 4]], [], [[1, 1]], [], [[1, 3], [-1, 9]], [], [[-1, 0], [-1, 4]], [], [[-1, 6], [1, 8]], [], [[-1, 1], [-1, 5]], [], [[-1, 9]], [], [[1, 6]], [], [[-1, 0], [2, 2], [-1, 2], [1, 6], [-1, 8]], [], [[1, 3]], [], [[-1, 7]], [], [[1, 0], [1, 4]], [], [[-1, 8]], [], [[1, 5], [-1, 7]], [], [[-1, 1], [1, 7]], [], [[-1, 6]], [], [[1, 0]], [], [[-1, 3], [1, 5], [1, 9]], [], [[1, 3]], [], [], [], [[1, 0], [1, 0], [1, 4], [-1, 6]], [], [], [], [[1, 7]], [], [[1, 2], [-1, 4], [1, 6], [-1, 8]], [], [], [], [[1, 1], [-1, 7]], [], [[1, 1], [1, 5], [-1, 7]], [], [[-1, 4]], [], [[1, 2]], [], [[1, 5], [1, 9]], [], [[-1, 3]], [], [], [], [[-1, 2], [-1, 6]], [], [[-1, 9]], [], [], [], [[1, 0], [-2, 2], [1, 2], [1, 4], [-1, 6], [1, 8]], [], [[-1, 2]], [], [[1, 3], [1, 7]], [], [[-1, 3], [1, 9]], [], [], [], [[1, 6]], [], [[1, 3], [1, 7]], [], [[1, 1], [1, 9]], [], [[-1, 2], [1, 4]], [], [[-1, 0], [-1, 4], [1, 6]], []]}