# Stored data for newform 3332.1.bc.c, downloaded from the LMFDB on 19 April 2024.
{"label": "3332.1.bc.c", "space_label": "3332.1.bc", "level": 3332, "weight": 1, "hecke_orbit": 3, "hecke_orbit_code": 9009123416870148, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 1630966273340867825, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [4, -4, 2, -2, 1]], [13, [0, 1]]], "qexp_display": "q-\\zeta_{12}q^{2}+\\zeta_{12}^{2}q^{4}+(\\zeta_{12}-\\zeta_{12}^{4}+\\cdots)q^{5}+\\cdots", "char_order": 12, "char_parity": -1, "char_degree": 4, "char_conductor": 476, "char_orbit_label": "bc", "char_is_real": false, "Nk2": 3332, "analytic_conductor": 1.662884622093164, "hecke_ring_index": 1, "level_radical": 238, "projective_image": "D4", "projective_image_type": "Dn", "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 12, "artin_degree": 96, "artin_image": "96.54", "field_poly_is_real_cyclotomic": false, "projective_field_label": "4.2.19652.1", "hecke_ring_index_proved": true, "self_twist_type": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.681", "prec": 17}, "analytic_rank_proved": true, "char_values": [3332, 12, [1667, 885, 785], [6, 4, 9]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 8, "level_primes": [2, 7, 17], "conrey_indexes": [667, 863, 2027, 2223], "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": "0.047", "prec": 17}, {"__RealLiteral__": 0, "data": "4.008", "prec": 17}, {"__RealLiteral__": 0, "data": "2.475", "prec": 17}, {"__RealLiteral__": 0, "data": "118.568", "prec": 24}, {"__RealLiteral__": 0, "data": "158.568", "prec": 24}, {"__RealLiteral__": 0, "data": "5880.156", "prec": 27}], "related_objects": [], "self_twist_discs": [-4], "cm_discs": [-4], "rm_discs": [], "relative_dim": 1, "trace_display": [0, 0, 2, 0], "traces": [0, 4, 0, 0, 2, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 2, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, -4, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -2, -4, 0, 2, -8, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 8, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -8, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 4, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 2, 0, -2, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 8, 0, 0, 0, 0, 0, 0, -8, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -8, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 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, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 2, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 8, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -8, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 8, 0, 0, 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, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, -2, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0], "projective_field": [-17, 0, 0, 0, 1], "artin_field": [1, -4, 14, 2, -83, 170, -1, -262, 234, -376, 1153, -338, -355, 364, 36, -452, -27, 272, 2, -104, 20, 24, -8, -2, 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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, -4], [1, 1, 7, 3, 1, 3, 0], [1, 1, 17, 3, 1, 4, 0], [1, 1, 28, 7, -1, 6, 0], [1, 1, 68, 6, -1, 4, 0], [1, 1, 119, 14, 1, 12, 0], [1, 1, 476, 28, -1, 12, 0]], "char_orbit_index": 29, "prim_orbit_index": 28, "minimal_twist": "68.1.f.a", "char_is_minimal": false, "conrey_index": 667, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "artin_field_label": null, "sato_tate_group": null, "atkin_lehner_eigenvals": null, "embedded_related_objects": null, "qexp": [[], [[1, 0]], [[-1, 1]], [], [[1, 2]], [[1, 1], [-1, 4]], [], [], [[-1, 3]], [[-1, 1]], [[-1, 2], [1, 5]], [], [], [], [], [], [[1, 4]], [[1, 2]], [[1, 2]], [], [[1, 0], [1, 3]], [], [], [], [], [[-1, 5]], [], [], [], [[1, 0], [1, 3]], [], [], [[-1, 5]], [], [[-1, 3]], [], [[-1, 3]], [[1, 1], [-1, 4]], [], [], [[-1, 1], [-1, 4]], [[1, 0], [-1, 3]], [], [], [], [[-1, 2], [1, 5]], [], [], [], [], [[-1, 0]], [], [], [], [], [], [], [], [[-1, 1], [-1, 4]], [], [], [[-1, 1], [-1, 4]], [], [], [[-1, 0]], [], [], [], [[1, 4]], [], [], [], [[1, 4]], [[-1, 2], [-1, 5]], [[-1, 2], [1, 5]], [], [], [], [], [], [[1, 2], [1, 5]], [[1, 2]], [[-1, 1], [1, 4]], [], [], [[1, 0], [1, 3]], [], [], [], [], [[1, 0], [1, 3]], [], [], [], [], [], [], [[-1, 0], [-1, 3]], [], [], [[1, 1]]]}