# Stored data for newform 462.2.a.h, downloaded from the LMFDB on 20 April 2024. {"label": "462.2.a.h", "space_label": "462.2.a", "level": 462, "weight": 2, "hecke_orbit": 8, "hecke_orbit_code": 31525197425148366, "dim": 2, "is_polredabs": true, "nf_label": "2.2.12.1", "trace_hash": 2010205270847360632, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [-12, 0, 1]], [13, [-2, 1]]], "qexp_display": "q-q^{2}+q^{3}+q^{4}+\\beta q^{5}-q^{6}+q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1848, "fricke_eigenval": -1, "atkin_lehner_string": "+---", "analytic_conductor": 3.6890885733831538, "hecke_ring_index": 2, "level_radical": 462, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 12, "field_poly_is_real_cyclotomic": true, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.042", "prec": 17}, "analytic_rank_proved": true, "char_values": [462, 1, [155, 199, 211], [1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [2, 3, 7, 11], "conrey_indexes": [1], "field_disc": 12, "field_disc_factorization": [[2, 2], [3, 1]], "field_poly": [-3, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.032", "prec": 17}, {"__RealLiteral__": 0, "data": "1.943", "prec": 17}, {"__RealLiteral__": 0, "data": "0.163", "prec": 17}, {"__RealLiteral__": 0, "data": "9.618", "prec": 17}, {"__RealLiteral__": 0, "data": "1.428", "prec": 17}, {"__RealLiteral__": 0, "data": "67.386", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [3, -1], [7, -1], [11, -1]], "trace_display": [-2, 2, 0, 2], "traces": [0, 2, -2, 2, 2, 0, -2, 2, -2, 2, 0, 2, 2, 4, -2, 0, 2, 0, -2, 4, 0, 2, -2, 0, -2, 14, -4, 2, 2, -12, 0, 4, -2, 2, 0, 0, 2, 4, -4, 4, 0, 0, -2, -8, 2, 0, 0, 12, 2, 2, -14, 0, 4, 12, -2, 0, -2, 4, 12, 0, 0, 4, -4, 2, 2, 0, -2, 16, 0, 0, 0, -24, -2, -8, -4, 14, 4, 2, -4, -8, 0, 2, 0, -12, 2, -24, 8, -12, -2, 12, 0, 4, 0, 4, -12, -24, -2, 4, -2, 2, 14, -12, 0, -20, -4, 0, -12, 0, 2, 4, 0, 4, 2, -12, -4, -48, -12, 4, 0, 0, 0, 2, -4, 0, 4, 0, -2, -8, -2, -8, 0, 12, 2, 4, -16, 0, 0, -12, 0, -20, 0, 12, 24, 4, 2, 0, 8, 2, 4, -12, -14, -32, -4, 0, -2, -24, 4, 16, 8, 12, 0, 0, -2, -8, 0, 0, 12, 24, -2, -18, 24, 4, -8, 12, 12, 14, 2, 0, -12, 0, 0, -8, -4, 4, 0, 48, -4, 0, 12, 2, 24, 0, 2, 52, -4, 0, 2, 36, -2, -20, -14, 16, 12, -12, 0, -24, 20, 0, 4, 4, 0, -8, 12, -24, 0, 48, -2, 4, -4, -8, 0, 0, -4, 4, -2, 14, 12, 12, 4, -8, 48, 2, 12, 12, -4, -24, 0, -8, 0, -48, 0, 40, -2, 2, 4, 0, 0, 8, -4, -12, 0, 48, 2, 0, 8, -24, 2, 12, 8, 4, 0, -12, -12, -24, -2, 48, -4, 12, 16, 0, 0, -8, 0, 4, 12, 14, 0, 4, 20, 4, 0, 12, -12, -20, -24, -24, -4, 0, -2, -10, 0, 4, -8, -36, -2, -48, -4, 2, 12, 0, 14, -8, 32, -12, 4, 0, 0, 28, 2, -20, 24, 36, -4, -20, -16, 0, -8, 12, -12, -12, 0, 0, 0, 24, 2, 28, 8, 4, 0, 12, 0, -32, -12, 4, -24, -48, 2, 28, 18, -12, -24, 4, -4, 2, 8, -48, -12, 0, -12, -20, -14, 4, -2, 12, 0, 0, 12, 0, 0, -24, 0, -6, 8, 2, 4, -24, -4, 4, 0, 0, -48, 12, 4, 4, 0, 0, -12, -24, -2, -8, -24, -8, 0, 36, -2, 0, -52, -8, 4, -60, 0, 48, -2, 12, -36, 48, 2, 16, 20, 4, 14, 36, -16, 8, -12, 0, 12, 4, 0, 16, 24, -12, -20, 0, 0, -72, -4, -20, -4, -72, 0, -20, 8, 12, -12, 0, 24, 4, 0, 4, -48, -24, 2, 4, -4, 0, 4, 48, 8, -8, 0, 2, 0, 0, 4, 48, -4, -12, 2, -12, -14, 0, -12, -32, -12, 0, -4, 4, 8, 0, -48, -12, -2, 16, -12, -24, -12, 24, 4, 16, 24, 16, 0, -8, 8, 28, 0, 12, 48, 0, 0, 8, -40, 0, 2, 0, -2, 40, -4, -8, 0, 24, 0, 0, -8, 0, 4, -24, 12, -32, 0, 24, -48, 24, -2, 96, 0, -18, -8, -48, 24, -8, -2, 4, -12, 24, -8, 12, -4, 12, 0, 60, 12, 28, 12, 14, 24, 24, 2, 50, -48, 0, 4, 0, -12, 48, -16, 0, 0, 2, 0, 4, 8, -8, 0, -96, -4, -32, -12, 4, -14, -24, 0, -8, -4, 48, -20, -12, -4, -16, 0, 0, -12, 12, 12, -96, 20, 2, 24, -36, 24, 16, 4, 0, 0, 0, 2, -20, 10, 52, 0, -12, -4, 12, 8, 0, 36, 0, 2, 32, 48, 36, 4, -48, -2, -24, -12, -20, 0, -24, -14, 16, 8, 16, -32, 0, 12, 16, -4, -12, 0, 24, 0, -44, -28, -24, -2, -12, 20, -8, -24, 0, -36, 12, 4, -22, 20, 4, 16, -48, 0, 40, 8, -8, -12, 48, 12, 4, 12, -24, 0, 36, 0, 16, 0, 48, -24, 36, -2, 0, -28, 4, -8, -12, -4, 72, 0, -8, -12, -48, 0, 40, 32, 0, 12, -24, -4, 0, 24, 4, 48, 4, -2, 28, -28, 14, -18, -36, 12, 4, 24, 12, -4, 48, 4, -96, -2, -8, -8, 24, 48, -80, 12, 2, 0, 24, 12, 24, 20, 12, 14, 36, -4, -40, 2, -24, -12, -12, 0, 52, 0, -8, -12, 48, 0, 0, 0, -48, 24, -12, 0, -20, 6, 40, -8, -84, -2, 4, -4, 2, 24, -48, 4, 52, -4, 0, 0, 16, 0, 16, 48, 8, -12, 0, -4, 0, -4, -12, 0, 0, 0, -8, 12, 48, 24, 0, 2, 4, 8, 0, 24, -72, 8, 4, 0, -24, -36, 0, 2, 64, 0, 12, 52, -72, 8, 28, -4, 4, 60, 24, 0, -24, -48, -12, 2, 72, -12, 4, 36, -24, -48, -12, -2, 8, -16, 48, -20, -72, -4, 24, -14, 12, -36, -8, 16, -48, -8, 0, 12, 36, 0, 28, -12, -8, -4, 0, 0, -64, -16, 4, -24, -12, 12, 40, 20, 14, 0, 24, 0, 40, 72, 4, 4, 0, 20, -48, 4, 4, 72, -60, 0, 14, 20, 12, -8, 0, -12, 2, 12, -20, 0, -96, -24, -44, -4, -24, 0, 24, -4, 64, 48, 0, 24, 48, -2, 48, -4, -10, 4, -8, 0, 32, -4, 4, -48, 0, -8, -92, 8, -36, 0, -12, -2, -56, 0, -48, 0, 48, -4, -8, -48, 2, 4, 48, 12, 144, -2, 0, 12, -24, 14, -48, 0, -8, 12, -72, 32, 16, 12, -12, 0, 0, 4, -12, -4, 0, -8, 12, 0, 16, 48, 28, 12, -48, 2, 28, -16, -20, 12, 12, 24, 4, 12, 36, -24, -24, -4, -8, -16, -20, -24, -36, -16, 48, 0, 0, 8, 72, -8, -16, -28, 12, 0, -12, -12, -144, -48, -12, 0, -12, 0, -30, -8, 0, 40, 0, 0, 64, -2, 24, 0, 24, 2, -20, -40, 28, 4, -12, 8, 12, 0, 4, -24, 12, 0, 0, 0, 12, 8, -96, 0, -32, -4, -32, 24, -72, -12, -20, 32, 4, 0], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "462.2.a.h", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [-1, 0], [1, 0], [1, 0], [0, 1], [-1, 0], [1, 0], [-1, 0], [1, 0], [0, -1], [1, 0], [1, 0], [2, 0], [-1, 0], [0, 1], [1, 0], [0, -1], [-1, 0], [2, -1], [0, 1], [1, 0], [-1, 0], [0, -2], [-1, 0], [7, 0], [-2, 0], [1, 0], [1, 0], [-6, 0], [0, -1], [2, -1], [-1, 0], [1, 0], [0, 1], [0, 1], [1, 0], [2, 2], [-2, 1], [2, 0], [0, -1], [0, -1], [-1, 0], [-4, 2], [1, 0], [0, 1], [0, 2], [6, -1], [1, 0], [1, 0], [-7, 0], [0, -1], [2, 0], [6, 2], [-1, 0], [0, 1], [-1, 0], [2, -1], [6, 0], [0, -2], [0, 1], [2, 0], [-2, 1], [1, 0], [1, 0], [0, 2], [-1, 0], [8, -2], [0, -1], [0, -2], [0, -1], [-12, 0], [-1, 0], [-4, -1], [-2, -2], [7, 0], [2, -1], [1, 0], [-2, 0], [-4, 2], [0, 1], [1, 0], [0, 1], [-6, -3], [1, 0], [-12, 0], [4, -2], [-6, 0], [-1, 0], [6, 2], [0, -1], [2, 0], [0, -2], [2, -1], [-6, 1], [-12, 2], [-1, 0], [2, 0], [-1, 0], [1, 0], [7, 0]]}