# Stored data for newform 567.2.e.a, downloaded from the LMFDB on 19 April 2024.
{"label": "567.2.e.a", "space_label": "567.2.e", "level": 567, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 274911461943, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 700283207121553302, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [1, 1, 1]]], "qexp_display": "q-\\zeta_{6}q^{2}+(1-\\zeta_{6})q^{4}+\\zeta_{6}q^{5}+(-2+\\cdots)q^{7}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "e", "char_is_real": false, "Nk2": 2268, "analytic_conductor": 4.527517794606598, "hecke_ring_index": 1, "level_radical": 21, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "field_poly_is_real_cyclotomic": false, "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": "0.015", "prec": 17}, "analytic_rank_proved": true, "char_values": [567, 3, [407, 325], [3, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [3, 7], "conrey_indexes": [163, 487], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.945", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.404", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "104.634", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [-1, 0, 1, -5], "traces": [0, 2, -1, 0, 1, 1, 0, -5, -6, 0, 1, -5, 0, -10, 1, 0, 1, -3, 0, -1, 2, 0, 10, -3, 0, 4, 5, 0, -4, -2, 0, 0, -5, 0, 6, -1, 0, -3, -1, 0, -3, -10, 0, -2, 5, 0, -3, 0, 0, 11, -8, 0, -5, 9, 0, -10, 15, 0, 1, 0, 0, 14, 0, 0, 14, -5, 0, -4, 3, 0, -4, -24, 0, -3, -3, 0, -2, 20, 0, -8, -1, 0, 5, -18, 0, -6, 1, 0, 15, 13, 0, 25, -6, 0, 0, 1, 0, -18, 2, 0, -4, 17, 0, 1, 30, 0, -18, -17, 0, 9, 5, 0, -1, -2, 0, 3, -1, 0, 0, 12, 0, -14, 14, 0, 0, 18, 0, -24, 3, 0, -5, 1, 0, 1, 8, 0, 9, 9, 0, 18, -5, 0, 12, 25, 0, -1, 6, 0, -6, -3, 0, -5, 3, 0, -25, 0, 0, 14, -8, 0, -10, 3, 0, 11, -5, 0, 9, -38, 0, 24, 3, 0, -1, 14, 0, -16, -10, 0, 13, -19, 0, -28, -5, 0, 9, 3, 0, -15, 0, 0, -2, -8, 0, 10, 9, 0, 13, 4, 0, -3, -12, 0, -34, 5, 0, -5, 1, 0, -5, 10, 0, 26, -9, 0, -17, -1, 0, 0, -18, 0, -5, 15, 0, 38, 20, 0, 1, 3, 0, 1, -6, 0, 6, -3, 0, 0, 0, 0, -15, -30, 0, -11, -14, 0, 28, -2, 0, 5, 0, 0, -9, -56, 0, 30, 12, 0, 17, 29, 0, 3, -10, 0, 1, -5, 0, 18, 4, 0, 4, -3, 0, -1, -6, 0, -18, 20, 0, -19, -9, 0, 3, -58, 0, -28, -12, 0, -50, 25, 0, 8, -1, 0, 3, -10, 0, 0, 9, 0, -3, 15, 0, 5, 10, 0, 1, -14, 0, 56, -5, 0, 0, 0, 0, -14, -28, 0, -16, 6, 0, 5, 7, 0, 12, 6, 0, -20, 11, 0, 30, 0, 0, -8, -9, 0, 19, -8, 0, -58, -12, 0, -3, 0, 0, -20, 6, 0, 14, -4, 0, 38, 20, 0, -25, -11, 0, -12, 26, 0, 38, 11, 0, 18, 14, 0, 20, -6, 0, 3, 3, 0, -6, -36, 0, 25, -15, 0, 0, 10, 0, -24, -1, 0, -8, -27, 0, 25, -20, 0, -9, 9, 0, 18, -33, 0, -2, 8, 0, -15, 6, 0, 8, -3, 0, 0, -17, 0, -1, 30, 0, -14, -5, 0, 2, 0, 0, -9, 25, 0, -5, 18, 0, -2, -13, 0, -27, 12, 0, -14, -34, 0, -1, 9, 0, -28, 0, 0, -9, -3, 0, 0, 30, 0, -30, -36, 0, -13, -19, 0, -35, 60, 0, 25, -1, 0, -6, 5, 0, -22, 1, 0, -3, 38, 0, 26, -1, 0, -3, 27, 0, 16, 0, 0, 0, 5, 0, -8, -3, 0, 15, -25, 0, 15, 22, 0, -28, -9, 0, -19, -42, 0, 13, 26, 0, 3, 5, 0, 0, 60, 0, -31, 9, 0, 28, 0, 0, 34, -15, 0, -12, 29, 0, 12, -22, 0, 29, -1, 0, 0, 12, 0, 15, -3, 0, -1, 2, 0, 10, 0, 0, 14, -9, 0, 5, 50, 0, 17, 12, 0, 6, -65, 0, 25, -1, 0, -15, 18, 0, -58, -9, 0, 20, 1, 0, 8, 38, 0, 9, 37, 0, 10, 4, 0, 29, 28, 0, -1, 56, 0, 72, 34, 0, -32, -25, 0, -5, -24, 0, -31, 8, 0, -2, 45, 0, 45, 9, 0, 5, -74, 0, 0, 0, 0, 3, -15, 0, 15, -6, 0, 15, 24, 0, -18, -1, 0, 5, 14, 0, 1, 10, 0, 28, 0, 0, -19, -28, 0, -60, 54, 0, -25, 0, 0, 0, -13, 0, -11, -14, 0, -14, 18, 0, -80, 24, 0, 6, -12, 0, -55, -10, 0, -3, 9, 0, -38, 15, 0, -3, -31, 0, 0, 40, 0, 22, -3, 0, -1, -5, 0, 0, 54, 0, 14, -8, 0, 54, -4, 0, 3, -19, 0, 4, -140, 0, -58, 29, 0, 12, -42, 0, 45, 18, 0, 0, 9, 0, 18, -17, 0, -1, -45, 0, 28, 28, 0, 8, 9, 0, 15, -19, 0, 4, 60, 0, -3, -35, 0, 22, -68, 0, 6, -12, 0, -39, 0, 0, 50, 19, 0, 11, 27, 0, -1, -36, 0, -14, -4, 0, 94, -75, 0, 3, 3, 0, -27, -6, 0, 30, -20, 0, 9, -3, 0, 45, -30, 0, 3, 25, 0, -30, 17, 0, -31, 0, 0, -5, -10, 0, 4, 12, 0, -3, -27, 0, -36, -16, 0, -27, 0, 0, 46, -5, 0, -10, -31, 0, 0, 54, 0, -18, 5, 0, 60, -9, 0, -2, 28, 0, -28, 2, 0, -16, 5, 0, -70, -15, 0, 3, 46, 0, 0, 20, 0, -3, -15, 0, -12, 0, 0, -51, 9, 0, -56, 4, 0, -15, -11, 0, 1, 28, 0, -10, -22, 0, 24, -3, 0, 0, -24, 0, 25, -9, 0, -70, -39, 0, -19, 5, 0, -9, -74, 0, -56, 1, 0, 13, 12, 0, 14, 18, 0, 12, -9, 0, -74, -56, 0, 51, -11, 0, 1, -2, 0, -18, 39, 0, -14, 14, 0, 0, 80, 0, 20, -27, 0, 6, -45, 0, 53, 0, 0, -5, -84, 0, 88, -15, 0, -36, 29, 0, 60, 26, 0, 19, 0, 0, -38, -3, 0, -30, 0, 0, 27, -50, 0, 6, -14, 0, -5, -3, 0, 20, 54, 0, 45, -22, 0, 2, -1, 0, -17, -9, 0, -19, 120, 0, -24, -13, 0, 5, 14, 0, 2, -6, 0, 27, 15, 0, 84, -20, 0, 0, 14, 0, 15, 0, 0, -10, 20, 0, 15, 4, 0, -36, -52, 0, 8, -15, 0, 50, -36, 0, 31, 15, 0, 11, 20, 0, 26, 42, 0, -9, -57, 0, -45, 38, 0, -14, -18, 0, -130, 11, 0, -13, 3, 0, 2, -6, 0, 10, 3, 0, 37, 0, 0, -12, -6, 0, 17, -31, 0, -54], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "63.2.g.a", "char_is_minimal": true, "conrey_index": 163, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [0, -1], [0, 0], [1, -1], [0, 1], [0, 0], [-2, -1], [-3, 0], [0, 0], [1, -1], [-5, 5], [0, 0], [-5, 0], [-1, 3], [0, 0], [0, 1], [-3, 3], [0, 0], [0, -1], [1, 0], [0, 0], [5, 0], [0, -3], [0, 0], [4, -4], [0, 5], [0, 0], [-3, 2], [-1, 0], [0, 0], [0, 0], [-5, 5], [0, 0], [3, 0], [1, -3], [0, 0], [0, -3], [-1, 1], [0, 0], [0, -3], [-5, 0], [0, 0], [-1, 0], [0, 5], [0, 0], [-3, 3], [0, 0], [0, 0], [3, 5], [-4, 0], [0, 0], [-5, 5], [9, -9], [0, 0], [-5, 0], [6, 3], [0, 0], [0, 1], [0, 0], [0, 0], [0, 14], [0, 0], [0, 0], [7, 0], [0, -5], [0, 0], [-4, 4], [0, 3], [0, 0], [-3, 2], [-12, 0], [0, 0], [-3, 3], [-3, 3], [0, 0], [-1, 0], [15, -10], [0, 0], [0, -8], [-1, 1], [0, 0], [0, 5], [-9, 0], [0, 0], [-3, 0], [0, 1], [0, 0], [15, -15], [0, 13], [0, 0], [10, 5], [-3, 0], [0, 0], [0, 0], [1, -1], [0, 0], [-9, 0], [5, -8], [0, 0], [0, -4]]}