# Stored data for newform 462.2.k.b, downloaded from the LMFDB on 19 April 2024.
{"label": "462.2.k.b", "space_label": "462.2.k", "level": 462, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504286855692750, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 1971015937492316688, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [144, 0, 12, 0, 1]], [17, [729, 0, 27, 0, 1]]], "qexp_display": "q+\\zeta_{12}q^{2}+(\\zeta_{12}+\\zeta_{12}^{3})q^{3}+\\zeta_{12}^{2}q^{4}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 21, "char_orbit_label": "k", "char_is_real": false, "Nk2": 1848, "analytic_conductor": 3.6890885733831538, "hecke_ring_index": 1, "level_radical": 462, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 12, "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": "0.593", "prec": 17}, "analytic_rank_proved": true, "char_values": [462, 6, [155, 199, 211], [3, 5, 6]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 4, "level_primes": [2, 3, 7, 11], "conrey_indexes": [89, 353], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.058", "prec": 17}, {"__RealLiteral__": 0, "data": "3.960", "prec": 17}, {"__RealLiteral__": 0, "data": "1.073", "prec": 17}, {"__RealLiteral__": 0, "data": "93.823", "prec": 20}, {"__RealLiteral__": 0, "data": "22.420", "prec": 20}, {"__RealLiteral__": 0, "data": "3137.154", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 0, 0, 8], "traces": [0, 4, 0, 0, 2, 0, 0, 8, 0, -6, 12, 0, 0, 0, 0, 24, -2, 0, 0, -18, 0, 0, -4, 0, -6, -14, 0, 0, 10, 0, 0, -12, 0, -6, 0, 0, -12, -14, 0, 0, 12, 0, 12, -20, 0, 0, -6, 0, 0, 4, 0, -18, 12, 0, -18, 0, 0, 0, -18, 0, 12, -12, 0, 6, -4, 0, 0, -16, 0, 0, 12, 0, 0, 48, 0, 0, 0, 0, 24, 32, 0, -18, 24, 0, 0, 72, 0, -54, -2, 0, 0, -24, 0, 0, -42, 0, -6, 0, 0, 0, 14, 0, 0, 36, 0, 48, 0, 0, 0, 16, 0, 0, 2, 0, 18, -36, 0, 36, 0, 0, 0, 2, 0, 24, -12, 0, 0, -28, 0, 0, -24, 0, 0, -54, 0, -36, -18, 0, 0, 0, 0, -84, 18, 0, -6, 108, 0, 0, -28, 0, 42, 34, 0, 0, -8, 0, 0, -30, 0, 0, 0, 0, 0, -4, 0, 0, 12, 0, -6, 4, 0, 54, -10, 0, 0, -70, 0, -6, 12, 0, 0, 0, 0, 0, 6, 0, -12, -18, 0, 0, -72, 0, 0, -8, 0, 0, 26, 0, 6, -12, 0, 0, 0, 0, -36, 48, 0, 0, 12, 0, 0, 16, 0, 54, -12, 0, 0, -12, 0, 0, -12, 0, -42, 0, 0, 84, 36, 0, 0, -48, 0, -18, -36, 0, 0, 84, 0, 0, 36, 0, -12, -72, 0, 0, 0, 0, 0, -36, 0, 12, -24, 0, -24, 12, 0, 0, -2, 0, 0, 14, 0, 0, 48, 0, 0, 0, 0, 24, 16, 0, 0, 36, 0, 0, -72, 0, 18, -16, 0, 0, 36, 0, 0, 36, 0, -108, 0, 0, 0, -20, 0, 0, 48, 0, 48, 24, 0, 18, -6, 0, 0, -40, 0, -42, 18, 0, -54, 0, 0, 0, -24, 0, 12, 42, 0, 0, 64, 0, 0, -18, 0, 0, -30, 0, 18, -84, 0, 0, 0, 0, -24, -44, 0, -42, 36, 0, 0, 112, 0, 108, 36, 0, 0, -40, 0, 0, 24, 0, -54, 0, 0, 0, 2, 0, 0, -108, 0, 18, -60, 0, -36, 16, 0, 0, 12, 0, 12, 120, 0, 0, 0, 0, 0, 68, 0, -24, -42, 0, -54, -80, 0, 0, 0, 0, 0, 24, 0, 30, 6, 0, 0, 0, 0, 96, -6, 0, 0, 90, 0, 0, 28, 0, 48, 24, 0, 0, 18, 0, 0, -48, 0, -108, 0, 0, 36, 24, 0, 0, 18, 0, 60, -76, 0, 0, 0, 0, 0, -36, 0, -12, -60, 0, 0, 0, 0, 0, -16, 0, 48, -30, 0, 66, 72, 0, 0, -24, 0, 0, -8, 0, 0, -24, 0, 0, 0, 0, 36, 16, 0, -54, -36, 0, 0, -16, 0, -72, 18, 0, 0, -80, 0, 0, -6, 0, 96, 0, 0, 0, -12, 0, 0, 84, 0, -36, 4, 0, 54, 76, 0, 0, -36, 0, -24, -162, 0, -36, 0, 0, 0, 64, 0, 36, -42, 0, 0, 168, 0, 0, -14, 0, 0, 48, 0, 0, -12, 0, 0, 0, 0, 48, 24, 0, -54, 60, 0, 0, -24, 0, 6, -28, 0, 0, -36, 0, 0, -72, 0, -90, 0, 0, -72, -40, 0, 0, -18, 0, 48, -172, 0, 36, 14, 0, 0, -32, 0, -84, -30, 0, 0, 0, 0, 0, 42, 0, -42, -216, 0, -90, 36, 0, 0, -10, 0, 0, 72, 0, 6, 96, 0, 0, 0, 0, 12, 0, 0, 0, 102, 0, 0, 72, 0, -18, -14, 0, 0, 144, 0, 0, -36, 0, 42, 0, 0, 96, -34, 0, 0, 60, 0, -54, -48, 0, 0, -4, 0, 0, -10, 0, -36, 60, 0, 54, 0, 0, 0, 22, 0, 18, -30, 0, 72, 56, 0, 0, 36, 0, 0, -96, 0, 0, -12, 0, 0, 0, 0, -120, 54, 0, 0, -6, 0, 0, -8, 0, -48, -96, 0, 0, -42, 0, 0, -138, 0, 108, 0, 0, 0, 54, 0, 0, -96, 0, -18, -104, 0, 0, 2, 0, 0, -12, 0, 60, 12, 0, 54, 0, 0, 0, 10, 0, -36, 180, 0, 0, 0, 0, 0, 72, 0, 0, -14, 0, -36, 126, 0, 0, 0, 0, -12, -38, 0, 96, 12, 0, 0, 48, 0, -36, 36, 0, 0, 108, 0, 0, 48, 0, 6, 0, 0, 108, 96, 0, 0, 12, 0, 24, 12, 0, -72, -40, 0, 0, 0, 0, 12, -36, 0, 0, 0, 0, 0, -8, 0, -42, 108, 0, 0, 148, 0, 0, -36, 0, 0, 80, 0, -108, -90, 0, 0, 0, 0, -24, 8, 0, 0, 84, 0, 0, -24, 0, 72, 18, 0, 0, 22, 0, 0, 54, 0, -36, 0, 0, 12, -24, 0, 0, -12, 0, -18, -252, 0, 0, 0, 0, 0, -36, 0, -48, -42, 0, -108, 0, 0, 0, 14, 0, -18, 90, 0, 108, 96, 0, 0, -64, 0, 0, 12, 0, 0, 18, 0, 0, 0, 0, -60, 72, 0, 0, -102, 0, 0, -208, 0, 126, 8, 0, 0, -2, 0, 0, 126, 0, 54, 0, 0, 0, 12, 0, 0, 12, 0, 120, -48, 0, 18, -48, 0, 0, -36, 0, -108, -96, 0, 18, 0, 0, 0, -28, 0, 102, -12, 0, 0, -80, 0, 0, -30, 0, 0, -56, 0, 0, 12, 0, 0, 0, 0, -72, -72, 0, 42, 0, 0, 0, 72, 0, -102, -56, 0, 0, -120, 0, 0, -12, 0, -72, 0, 0, 0, -98, 0, 0, 54, 0, -12, 196, 0, -108, -18, 0, 0, -90, 0, 18, 90, 0, 0, 0, 0, 0, -84, 0, -30, -72, 0, 36, 20, 0, 0, -96, 0, 0, -18, 0, 0, 0, 0, 0, 0, 0, -24, -38, 0, 0, -72, 0, 0, 92, 0, 162, -12, 0, 0, 60, 0, 0, 12, 0, -12, 0, 0, -96, -36, 0, 0, 36, 0, -168, -72, 0, 0, 40, 0, 0, -18, 0, -12, -108, 0, 0, 0], "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, 3, 2, -1, 2, 0], [1, 1, 7, 4, -1, 6, 0], [1, 1, 21, 7, 1, 6, 0]], "char_orbit_index": 11, "prim_orbit_index": 7, "minimal_twist": "462.2.k.b", "char_is_minimal": true, "conrey_index": 89, "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, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 1, 0, 1], [0, 0, 1, 0], [0, 2, 0, -4], [-1, 0, 2, 0], [3, 0, -2, 0], [0, 0, 0, 1], [-3, 0, 3, 0], [4, 0, -2, 0], [0, -1, 0, 1], [0, -1, 0, 2], [2, 0, -4, 0], [0, 3, 0, -2], [6, 0, 0, 0], [-1, 0, 1, 0], [0, 3, 0, 3], [0, -3, 0, 3], [-3, 0, -3, 0], [0, 4, 0, -2], [0, 5, 0, -1], [-1, 0, 0, 0], [0, -3, 0, 0], [-2, 0, 1, 0], [0, 0, -7, 0], [0, 2, 0, -4], [0, -6, 0, 3], [2, 0, 1, 0], [0, 0, 0, 9], [0, 6, 0, 0], [-4, 0, 2, 0], [0, -1, 0, 1], [-1, 0, -1, 0], [-3, 0, 6, 0], [0, -2, 0, -8], [-3, 0, 0, 0], [-7, 0, 7, 0], [0, -3, 0, -3], [0, 6, 0, -6], [2, 0, 2, 0], [0, 8, 0, -4], [1, 0, 4, 0], [-5, 0, 0, 0], [0, -1, 0, 0], [0, 6, 0, 6], [0, 0, -3, 0], [0, -7, 0, 14], [0, -2, 0, 1], [5, 0, -8, 0], [0, 0, 0, -7], [-9, 0, 9, 0], [4, 0, -2, 0], [0, 0, 0, 0], [-3, 0, -3, 0], [-2, 0, 4, 0], [0, 2, 0, 1], [0, 0, 0, -9], [-9, 0, 9, 0], [0, 1, 0, 1], [0, 0, 6, 0], [-2, 0, -2, 0], [0, -4, 0, 2], [-3, 0, 9, 0], [-1, 0, 0, 0], [0, -12, 0, 0], [0, -1, 0, -1], [0, 0, -8, 0], [0, -3, 0, 6], [3, 0, -6, 0], [8, 0, -10, 0], [0, 0, 0, -9], [0, -3, 0, 0], [16, 0, -8, 0], [0, -7, 0, 7], [0, 7, 0, -14], [3, 0, -6, 0], [0, -1, 0, 3], [6, 0, 0, 0], [16, 0, -16, 0], [0, 2, 0, 2], [0, 0, -9, 0], [4, 0, 4, 0], [0, 4, 0, -2], [0, 1, 0, 4], [18, 0, 0, 0], [0, -5, 0, 0], [-18, 0, 9, 0], [0, 0, -1, 0], [0, 2, 0, -4], [-6, 0, 12, 0], [-2, 0, -8, 0], [0, 0, 0, -3], [0, -6, 0, 0], [-14, 0, 7, 0], [0, -18, 0, 18], [-1, 0, -1, 0], [1, 0, -2, 0], [0, 5, 0, -8], [0, 0, 0, -3], [7, 0, -7, 0]]}