# Stored data for newform 1045.1.k.a, downloaded from the LMFDB on 28 January 2023. {"level_primes": [5, 11, 19], "is_polredabs": true, "rm_discs": [209], "conrey_indexes": [208, 417], "cm_discs": [], "trace_hash": 473357980046855311, "projective_field": [71, -6, 16, -1, 1], "level_radical": 1045, "hecke_ring_index_proved": true, "self_twist_type": 2, "related_objects": [], "prim_orbit_index": 11, "is_cm": false, "hecke_orbit": 1, "analytic_conductor": 0.5215229382014875, "inner_twist_count": 4, "field_disc_factorization": [[-1, 1], [2, 2]], "is_rm": true, "char_order": 4, "level_is_square": false, "weight_parity": -1, "label": "1045.1.k.a", "field_poly_is_real_cyclotomic": false, "is_self_twist": true, "is_twist_minimal": true, "minimal_twist": "1045.1.k.a", "projective_image_type": "Dn", "field_poly_is_cyclotomic": true, "dim": 2, "trace_zratio": {"__RealLiteral__": 0, "data": "0.700", "prec": 17}, "traces": [0, 2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 2, 0, 0, 2, 0, -2, 0, 2, 0, -2, -2, 0, -2, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, -2, 4, -2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 4, -2, 0, 0, 0, 2, 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, 0, 0, 0, 0, 2, 0, 0, -2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, -2, 0, 0, 2, 0, 2, 0, 0, 2, -4, 0, -2, 0, 0, 2, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, -2, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 4, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 2, 0, 0, 0, -2, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, -2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, -2, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 2, -4, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 4, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 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, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 2, -2, 0, 0, 0, 2, 0, 0, 2, -2, 0, 4, 0, 0, -6, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, -2, -2, 0, 0, -4, 2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 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, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, -4, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 2, 0, 2, 0, 0, 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, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 2, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, -4, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 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, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 4, 4, 0, 0, 4, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, -2, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, -2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 2, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 6, 0, 0, -2, 0, 0, 0, 0, 2, 0, -2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, -2, 0, 0, -4, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, -4, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, -4, -2, -2, 0, 0, 0, -2, 0, 0, 0, 2, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 0, 0, -4, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0], "hecke_ring_index_factorization": [], "nf_label": "2.0.4.1", "field_poly": [1, 0, 1], "has_non_self_twist": 1, "char_values": [1045, 4, [837, 761, 496], [3, 2, 2]], "Nk2": 1045, "field_poly_root_of_unity": 4, "analytic_rank": 0, "char_orbit_label": "k", "weight": 1, "trace_display": [-2, 0, 0, 0], "analytic_rank_proved": true, "char_parity": -1, "level_is_squarefree": true, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q+(-1-i)q^{2}+iq^{4}-iq^{5}-q^{8}+\\cdots", "self_twist_discs": [209], "char_is_real": false, "field_disc": -4, "level_is_prime_power": false, "relative_dim": 1, "hecke_cutters": [[2, [2, 2, 1]], [7, [0, 1]]], "space_label": "1045.1.k", "level": 1045, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 209, 4, 1, 2, 209], [1, 1, 5, 3, -1, 4, 0], [1, 1, 1045, 11, -1, 4, 0]], "char_degree": 2, "char_conductor": 1045, "char_orbit_index": 11, "hecke_ring_generator_nbound": 2, "projective_image": "D4", "hecke_orbit_code": 687211545621, "projective_field_label": "4.0.26125.1", "trace_moments": [{"__RealLiteral__": 0, "data": "-0.002", "prec": 20}, {"__RealLiteral__": 0, "data": "1.817", "prec": 17}, {"__RealLiteral__": 0, "data": "0.039", "prec": 17}, {"__RealLiteral__": 0, "data": "17.167", "prec": 20}, {"__RealLiteral__": 0, "data": "0.903", "prec": 17}, {"__RealLiteral__": 0, "data": "227.051", "prec": 24}], "id": null, "sato_tate_group": null, "embedded_related_objects": null, "artin_image": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "artin_field": null, "artin_field_label": null, "fricke_eigenval": null, "artin_degree": null, "qexp": [[], [[1, 0]], [[-1, 0], [-1, 1]], [], [[1, 1]], [[-1, 1]], [], [], [[1, 0], [-1, 0]], [[-1, 1]], [[-1, 0], [1, 1]], [[1, 0]], [], [[1, 0], [-1, 1]], [], [], [[1, 0]], [], [[-1, 0], [1, 1]], [[1, 1]], [[1, 0]], [], [[-1, 0], [-1, 1]], [[-1, 0], [1, 1]], [], [[-1, 0]], [[-1, 0], [-1, 0]], [], [], [[-1, 1], [-1, 1]], [], [], [[-1, 0], [-1, 1]], [], [], [], [[1, 0]], [], [[1, 0], [-1, 1]], [], [], [], [], [], [[1, 1]], [[-1, 0]], [[1, 0], [1, 0]], [[-1, 0], [-1, 1]], [], [[1, 1]], [[1, 0], [1, 1]], [], [[1, 0], [1, 1]], [], [], [[-1, 1]], [], [], [[-2, 0], [2, 1]], [], [], [], [], [], [[1, 1]], [[-1, 0], [-1, 1]], [], [], [], [], [], [], [], [], [], [], [[-1, 0]], [], [], [], [[-1, 1]], [[-1, 0]], [], [], [], [], [], [], [], [], [[1, 0], [1, 1]], [], [[-1, 0], [-1, 1]], [], [[1, 0], [-1, 0], [2, 1]], [[1, 0]], [], [], [[1, 0], [-1, 1]], [[-1, 1]], [[-1, 1]]]}