# Stored data for newform 31.1.b.a, downloaded from the LMFDB on 30 March 2023. {"level_primes": [31], "is_polredabs": true, "rm_discs": [], "conrey_indexes": [30], "cm_discs": [-31], "trace_hash": 58047233262006326, "projective_field": [-1, 1, 0, 1], "level_radical": 31, "hecke_ring_index_proved": true, "self_twist_type": 1, "related_objects": ["ArtinRepresentation/2.31.3t2.1"], "prim_orbit_index": 2, "is_cm": true, "hecke_orbit": 1, "embedded_related_objects": [["ArtinRepresentation/2.31.3t2.1c1"]], "analytic_conductor": 0.015471015391623074, "inner_twist_count": 2, "field_disc_factorization": [], "is_rm": false, "char_order": 2, "level_is_square": false, "weight_parity": -1, "label": "31.1.b.a", "field_poly_is_real_cyclotomic": false, "is_self_twist": true, "is_twist_minimal": true, "minimal_twist": "31.1.b.a", "projective_image_type": "Dn", "field_poly_is_cyclotomic": false, "dim": 1, "trace_zratio": {"__RealLiteral__": 0, "data": "0.507", "prec": 17}, "traces": [0, 1, -1, 0, 0, -1, 0, -1, 1, 1, 1, 0, 0, 0, 1, 0, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, -1, -1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, -1, -1, 1, 0, 0, 2, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 1, -1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, -1, 0, 0, 2, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 1, -1, 0, 0, 1, 1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, -1, -2, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 1, 1, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, -2, 2, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, 2, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 1, -1, 0, 1, -2, -1, -1, 0, 0, 0, 0, 0, -1, 0, 1, 2, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, -2, 1, 0, 2, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 1, 0, -1, -2, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 1, 0, 0, -1, -2, -1, 0, 0, 0, 0, 0, 2, 0, 1, -1, 2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, -1, 0, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, -1, 0, 1, 0, 0, 1, 0, -1, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 2, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -2, -2, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 1, 2, 1, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 1, -1, 0, 0, -1, 1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, -1, 0, 1, 1, 0, 0, 0, -1, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, -1, 0, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, -2, 0, 2, -2, 0, -1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, -1, 0, -2, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 1, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 1, 0, -1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, -1, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, -1, -1, 0, 0, 0, 0, 0, -2, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 2, 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, -1, 1, 0, 2, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 2, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, -1, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, -1, 0, 1, 0, -2, -1, 0, 0, 0, -1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, -1, -1, 0, 0, 0, 2, 0, 0, 1, -2, 1, 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, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 1, -2, 0, 0, -1, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, -1], "hecke_ring_index_factorization": [], "artin_image": "6.1", "nf_label": "1.1.1.1", "field_poly": [0, 1], "has_non_self_twist": 0, "char_values": [31, 2, [3], [1]], "Nk2": 31, "field_poly_root_of_unity": 0, "analytic_rank": 0, "char_orbit_label": "b", "weight": 1, "trace_display": [-1, 0, -1, -1], "analytic_rank_proved": true, "char_parity": -1, "level_is_squarefree": true, "hecke_ring_index": 1, "artin_field": [-1, 1, 0, 1], "level_is_prime": true, "char_is_minimal": true, "qexp_display": "q-q^{2}-q^{5}-q^{7}+q^{8}+q^{9}+q^{10}+\\cdots", "self_twist_discs": [-31], "char_is_real": true, "field_disc": 1, "level_is_prime_power": true, "relative_dim": 1, "hecke_cutters": [], "space_label": "31.1.b", "level": 31, "is_self_dual": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 31, 2, -1, 2, -31]], "char_degree": 1, "char_conductor": 31, "char_orbit_index": 2, "hecke_ring_generator_nbound": 1, "projective_image": "D3", "artin_field_label": "3.1.31.1", "hecke_orbit_code": 68736253983, "projective_field_label": "3.1.31.1", "trace_moments": [{"__RealLiteral__": 0, "data": "-0.013", "prec": 20}, {"__RealLiteral__": 0, "data": "0.972", "prec": 17}, {"__RealLiteral__": 0, "data": "0.945", "prec": 17}, {"__RealLiteral__": 0, "data": "2.886", "prec": 17}, {"__RealLiteral__": 0, "data": "4.773", "prec": 17}, {"__RealLiteral__": 0, "data": "10.544", "prec": 20}], "artin_degree": 6, "id": null, "sato_tate_group": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "fricke_eigenval": null, "qexp": [[0], [1], [-1], [0], [0], [-1], [0], [-1], [1], [1], [1], [0], [0], [0], [1], [0], [-1], [0], [-1], [-1], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [1], [0], [0], [0], [1], [0], [0], [1], [0], [-1], [-1], [0], [0], [0], [-1], [0], [2], [0], [0], [0], [0], [0], [0], [0], [0], [-1], [0], [0], [-1], [0], [0], [-1], [-1], [1], [0], [0], [2], [0], [0], [-1], [-1], [1], [0], [0], [0], [0], [0], [0], [0], [1], [1], [1], [0], [0], [0], [0], [0], [0], [0], [1], [0], [0], [0], [-2], [1], [0], [-1], [0], [0], [0]]}