# Stored data for newform 2563.1.b.d, downloaded from the LMFDB on 25 April 2024.
{"label": "2563.1.b.d", "space_label": "2563.1.b", "level": 2563, "weight": 1, "hecke_orbit": 4, "hecke_orbit_code": 13510867618368003, "dim": 2, "is_polredabs": true, "nf_label": "2.0.8.1", "trace_hash": 904506934093919639, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [2, 0, 1]], [17, [1, 1]]], "qexp_display": "q-\\beta q^{2}+\\beta q^{3}-q^{4}-\\beta q^{5}+2q^{6}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 2563, "char_orbit_label": "b", "char_is_real": true, "Nk2": 2563, "analytic_conductor": 1.2791036273783851, "hecke_ring_index": 1, "level_radical": 2563, "projective_image": "S4", "projective_image_type": "S4", "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "artin_degree": 48, "artin_image": "48.29", "field_poly_is_real_cyclotomic": false, "artin_field_label": "8.2.16836267547.1", "projective_field_label": "4.2.2563.1", "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.601", "prec": 17}, "analytic_rank_proved": true, "char_values": [2563, 2, [1399, 2333], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [11, 233], "conrey_indexes": [2562], "field_disc": -8, "field_disc_factorization": [[-1, 1], [2, 3]], "field_poly": [2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.066", "prec": 17}, {"__RealLiteral__": 0, "data": "2.062", "prec": 17}, {"__RealLiteral__": 0, "data": "0.265", "prec": 17}, {"__RealLiteral__": 0, "data": "15.720", "prec": 20}, {"__RealLiteral__": 0, "data": "1.058", "prec": 17}, {"__RealLiteral__": 0, "data": "182.412", "prec": 24}], "related_objects": ["ArtinRepresentation/2.11_233.24t22.1"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "trace_display": [0, 0, 0, 0], "traces": [0, 2, 0, 0, -2, 0, 4, 0, 0, -2, -4, -2, 0, 0, 0, 4, -2, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 2, -4, 0, 0, -2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, -4, 0, 0, 0, 2, 0, -4, 0, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 4, 0, 2, 4, 0, 2, 0, 4, -4, -4, 0, 0, 2, 2, 0, -4, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0, -4, 0, 0, 2, -4, 0, 0, -2, -2, -4, 2, 0, 2, 0, 0, 0, -2, 0, 4, 4, 0, 0, 0, 2, -4, 0, 0, 0, 2, 4, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 2, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 2, 0, 2, -4, 2, 4, 0, 0, 2, 0, 4, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 2, 0, -4, 2, 0, 4, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, 4, -4, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, -4, 0, 2, -4, 0, 0, 0, 0, -2, 0, 0, -2, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 2, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, -4, 0, 0, -2, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, -4, -2, 0, -2, 0, 0, 0, 0, 4, -2, 0, -2, 0, 2, 0, 0, -4, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, -4, -4, 0, 0, -4, -4, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, -4, 0, 4, 0, -2, 0, -2, 4, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, -2, -8, 0, 0, -4, 0, 2, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 2, 4, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, -2, 2, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, 2, -2, 0, 0, 0, 0, 0, 0, -4, 0, 4, 2, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, -2, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, -2, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 2, 0, 4, -2, 0, 2, -4, -2, 0, -2, -4, 4, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 4, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -4, 0, 0, 0, 4, 0, 0, -2, 0, 0, -2, 0, -4, 0, 0, 0, 0, -2, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, -4, 2, 0, 4, -4, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, -2, -2, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 4, 4, -2, -4, 4, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 4, 0, 0, -2, -4, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 2, 0, 4, -2, -2, 4, 0, 0, -2, 0, 2, 4, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, -2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, -4, -2, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 2, 0, 0, -4, 0, -4, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -2, -4, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 2, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 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, 4, 0, 2, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 2, -2, 4, 4, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 4, 4, -2, 0, 0, -2, 0, 0, 0, 0, 0, 2, 4, 0, 0, 2, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 8, 0, 2, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, 0, 0, -2, 0, 0, -4, 0, 4, 0, -2, 0, 0, 0, 0, 0, -2, 4, 0, -2, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, -2, 4, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -8, 2, 0, 0, 0, 4, 0, -2, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 4, 2, -4, 0, 0, 0, 0, 2, 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, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 4, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, -4, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, -4, 0, 0, -2, 2, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 4, 0, -2, 0, 0, 0, -2, 0, 4, 2, 0, 2, 0, 4, 0, 2, 4, 0, 0, -4, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, -4, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, -4, -2, 4, -2, -4, 2, 0, 0, 0, 2, -2, 0, -4, -2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, -4, 0, 0, 0, -2, 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, 0, 4, 0, 0, 0, 0, -2, 0, 2, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0], "projective_field": [-1, -1, 4, -2, 1], "artin_field": [-41, -75, -60, 1, 13, -4, -4, 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, 2563, 2, -1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "embedded_related_objects": [["ArtinRepresentation/2.11_233.24t22.1c1"], ["ArtinRepresentation/2.11_233.24t22.1c2"]], "minimal_twist": "2563.1.b.c", "char_is_minimal": true, "conrey_index": 2562, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "sato_tate_group": null, "atkin_lehner_eigenvals": null, "qexp": [[0, 0], [1, 0], [0, -1], [0, 1], [-1, 0], [0, -1], [2, 0], [0, 0], [0, 0], [-1, 0], [-2, 0], [-1, 0], [0, -1], [0, 0], [0, 0], [2, 0], [-1, 0], [-1, 0], [0, 1], [0, -1], [0, 1], [0, 0], [0, 1], [-1, 0], [0, 0], [-1, 0], [0, 0], [0, 0], [0, 0], [0, -1], [0, -2], [-1, 0], [0, 1], [0, -1], [0, 1], [0, 0], [1, 0], [1, 0], [-2, 0], [0, 0], [0, 0], [-1, 0], [0, 0], [1, 0], [1, 0], [0, 1], [0, 1], [0, 1], [0, -1], [1, 0], [0, 1], [0, -1], [0, 0], [0, -1], [0, 0], [0, 1], [0, 0], [2, 0], [-2, 0], [0, 0], [-2, 0], [0, 0], [0, 1], [0, 0], [1, 0], [0, 0], [-2, 0], [0, 0], [1, 0], [0, -1], [0, 0], [-1, 0], [0, 0], [1, 0], [0, -1], [0, -1], [0, 1], [0, 0], [0, 0], [-1, 0], [0, 1], [-1, 0], [0, 1], [0, 0], [0, 0], [0, 1], [0, -1], [2, 0], [0, 0], [1, 0], [2, 0], [0, 0], [1, 0], [0, -1], [2, 0], [-2, 0], [-2, 0], [0, -1], [0, -1], [1, 0], [1, 0]]}