# Stored data for newform 2005.1.g.a, downloaded from the LMFDB on 25 April 2024. {"label": "2005.1.g.a", "space_label": "2005.1.g", "level": 2005, "weight": 1, "hecke_orbit": 1, "hecke_orbit_code": 412333639637, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 1935824746415970027, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [2, -2, 1]]], "qexp_display": "q+(1-i)q^{2}-iq^{4}+q^{5}+(-1+i+\\cdots)q^{7}+\\cdots", "char_order": 4, "char_parity": -1, "char_degree": 2, "char_conductor": 2005, "char_orbit_label": "g", "char_is_real": false, "Nk2": 2005, "analytic_conductor": 1.0006253503291698, "hecke_ring_index": 1, "level_radical": 2005, "projective_image": "D4", "projective_image_type": "Dn", "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "field_poly_is_real_cyclotomic": false, "projective_field_label": "4.0.20100125.1", "hecke_ring_index_proved": true, "self_twist_type": 2, "is_self_dual": false, "is_self_twist": true, "is_cm": false, "is_rm": true, "trace_zratio": {"__RealLiteral__": 0, "data": "0.688", "prec": 17}, "analytic_rank_proved": true, "char_values": [2005, 4, [402, 1206], [1, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 4, "level_primes": [5, 401], "conrey_indexes": [1202, 1603], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.010", "prec": 17}, {"__RealLiteral__": 0, "data": "1.949", "prec": 17}, {"__RealLiteral__": 0, "data": "0.132", "prec": 17}, {"__RealLiteral__": 0, "data": "19.004", "prec": 20}, {"__RealLiteral__": 0, "data": "2.023", "prec": 17}, {"__RealLiteral__": 0, "data": "255.315", "prec": 24}], "related_objects": [], "self_twist_discs": [401], "cm_discs": [], "rm_discs": [401], "relative_dim": 1, "trace_display": [2, 0, 2, -2], "traces": [0, 2, 2, 0, 0, 2, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 2, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -4, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, -2, 0, -2, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 2, -2, 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, 0, 0, 0, 2, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 4, 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, 0, 0, -2, 0, 0, 2, 2, 0, 0, 0, -2, 8, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 2, 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, 4, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 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, 2, 0, 0, -2, 0, 0, -2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 0, -4, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 4, 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, -2, 0, 0, 0, 2, -4, 0, 0, 0, 0, 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, -2, 0, 0, -4, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 4, -2, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 4, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -6, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, -2, 4, 4, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, -4, 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, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 4, 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, -2, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, -2, 4, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 2, 4, 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, 0, 2, 0, 0, 2, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, -2, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -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, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 2, 0, 0, 8, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 2, 0, -4, 0, 2, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 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, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, -2, -6, 0, 0, -2, 0, -4, 0, 0, 2, 0, -2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 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, -4, 0, 2, 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, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, -4, -2, 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, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 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, -2, 0, 2, -2, 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, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2], "projective_field": [5, 0, 45, 0, 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, 401, 2, 1, 2, 401], [1, 1, 5, 3, -1, 4, 0], [1, 1, 2005, 7, -1, 4, 0]], "char_orbit_index": 7, "prim_orbit_index": 7, "minimal_twist": "2005.1.g.a", "char_is_minimal": true, "conrey_index": 1202, "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, 0], [-1, 1]], [], [[-1, 1]], [[1, 0]], [], [[-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, 0]], [], [], [[1, 0], [1, 1]], [[-1, 1], [-1, 1]], [], [], [[1, 0], [-1, 1]], [], [], [[-1, 0], [1, 1]], [[1, 0]], [], [], [], [], [], [], [[-1, 0], [-1, 1]], [], [[1, 1]], [], [[-1, 0], [1, 1]], [], [[-1, 1]], [[1, 0], [-1, 1]], [], [], [], [], [], [], [], [[-2, 0], [-2, 1]], [], [], [], [], [[-1, 0], [-1, 1]], [[-1, 1]], [], [], [], [], [], [[-1, 0], [1, 0], [2, 1]], [], [], [[-1, 0], [-1, 1]], [], [], [], [], [], [], [[1, 0]], [[-1, 0]], [], [[1, 0], [1, 1]], [], [], [[-1, 0], [-1, 0]], [], [], [], [[1, 0], [1, 1]], [], [], [], [[-1, 0], [1, 0], [2, 1]], [], [], [], [[-1, 0], [-1, 1]], [], [[-1, 1]]]}