# Stored data for newform 1045.1.w.b, downloaded from the LMFDB on 20 April 2024.
{"label": "1045.1.w.b", "space_label": "1045.1.w", "level": 1045, "weight": 1, "hecke_orbit": 2, "hecke_orbit_code": 4505111472636949, "dim": 4, "is_polredabs": true, "nf_label": "4.0.125.1", "trace_hash": 656850679054377362, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [0, 1]], [7, [5, 10, 10, 5, 1]]], "qexp_display": "q+\\zeta_{10}q^{4}-\\zeta_{10}q^{5}+(-1+\\zeta_{10}^{2}+\\cdots)q^{7}+\\cdots", "char_order": 10, "char_parity": -1, "char_degree": 4, "char_conductor": 1045, "char_orbit_label": "w", "char_is_real": false, "Nk2": 1045, "analytic_conductor": 0.5215229382014875, "hecke_ring_index": 1, "level_radical": 1045, "projective_image": "D10", "projective_image_type": "Dn", "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 10, "field_poly_is_real_cyclotomic": false, "projective_field_label": "10.2.87298324158753125.2", "hecke_ring_index_proved": true, "self_twist_type": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.682", "prec": 17}, "analytic_rank_proved": true, "char_values": [1045, 10, [837, 761, 496], [5, 6, 5]], "hecke_ring_generator_nbound": 4, "inner_twist_count": 4, "level_primes": [5, 11, 19], "conrey_indexes": [284, 379, 664, 949], "field_disc": 125, "field_disc_factorization": [[5, 3]], "field_poly": [1, -1, 1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "-0.025", "prec": 20}, {"__RealLiteral__": 0, "data": "3.681", "prec": 17}, {"__RealLiteral__": 0, "data": "-0.317", "prec": 20}, {"__RealLiteral__": 0, "data": "85.089", "prec": 20}, {"__RealLiteral__": 0, "data": "12.640", "prec": 20}, {"__RealLiteral__": 0, "data": "3065.549", "prec": 27}], "related_objects": [], "self_twist_discs": [-19], "cm_discs": [-19], "rm_discs": [], "relative_dim": 1, "trace_display": [0, 0, -1, -5], "traces": [0, 4, 0, 0, 1, -1, 0, -5, 0, 1, 0, 1, 0, 0, 0, 0, -1, 5, 0, -1, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 4, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -3, 0, -5, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -1, -1, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -5, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -4, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 3, 4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, -1, -3, 0, 0, -5, 0, 0, 2, 0, 5, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, -5, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, -5, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 5, 0, 5, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 5, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -5, 0, 0, -3, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -1, 0, 0, 0, -3, 1, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -6, 0, 0, 5, 0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 3, 5, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -5, -1, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, -5, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 5, 0, 0, 2, 0, 0, 0, -3, 0, 0, 0, 0, -5, 2, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -5, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -5, 0, 0, 0, 0, 0, 5, 0, 0, 0, -2, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 5, 0, 0, 0, 0, 0, -5, 0, 1, 0, 0, 0, -2, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 1, -8, 0, -5, 0, 0, 0, 0, 0, 0, 0, -4, 0, 5, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 5, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, -1, -5, 0, 0, -5, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 5, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 3, 0, 5, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -5, 0, 0, 0, 5, 0, 0, 0, 0, 0, 5, 0, 0, 3, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, -1, 0, 0, -5, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 6, 0, 0, 2, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, -5, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 5, 0, 0, -2, 0, 0, 0, 2, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -5, 0, 0, 0, -1, 0, 0, 0, 0, -3, 0, 5, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 1, 0, 0, 0, 0, 0, -5, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 5, -5, 0, 1, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -3, 0, 0, 1, -6, 0, 0, 0, 5, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 5, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -5, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, -2, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, -5, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 2, 0, 0, 3, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, -3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, -5, 0, 2, 0, 0, 0, 0, -1, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 2, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, -3, 0, 0, 0, 0, -6, 0, 0, -5, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 5, 0, 0, 0, 0, 0, 3, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 1, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, -2, 0, 0, 2, 4], "projective_field": [-1629, -213, 1459, 806, -145, -139, 173, 26, -19, -1, 1], "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, 19, 2, -1, 2, -19], [1, 1, 55, 10, 1, 10, 0], [1, 1, 1045, 23, -1, 10, 0]], "char_orbit_index": 23, "prim_orbit_index": 23, "minimal_twist": "1045.1.w.b", "char_is_minimal": true, "conrey_index": 284, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "sato_tate_group": null, "atkin_lehner_eigenvals": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[], [[1, 0]], [], [], [[1, 1]], [[-1, 1]], [], [[-1, 0], [1, 2]], [], [[1, 3]], [], [[-1, 4]], [], [], [], [], [[1, 2]], [[1, 0], [-1, 4]], [], [[1, 4]], [[-1, 2]], [], [], [[1, 2], [1, 3]], [], [[1, 2]], [], [], [[-1, 1], [1, 3]], [], [], [], [], [], [], [[1, 1], [-1, 3]], [[1, 4]], [], [], [], [], [], [], [[-1, 2], [-1, 3]], [[1, 0]], [[-1, 4]], [], [[-1, 1], [-1, 2]], [], [[1, 0], [-1, 2], [1, 4]], [], [], [], [], [], [[-1, 0]], [], [], [], [], [], [[-1, 0], [-1, 4]], [], [[-1, 0], [-1, 3]], [[1, 3]], [], [], [], [[1, 0], [1, 1]], [], [], [], [], [], [], [], [[-1, 0]], [[1, 1], [1, 4]], [], [], [[-1, 3]], [[-1, 1]], [], [[1, 1], [-1, 3]], [], [[-1, 0], [-1, 1]], [], [], [], [], [], [], [[1, 3], [1, 4]], [], [], [[1, 0]], [], [], [], [[1, 2]], [[1, 3]]]}