# Stored data for newform 3332.1.be.c, downloaded from the LMFDB on 19 April 2024. {"label": "3332.1.be.c", "space_label": "3332.1.be", "level": 3332, "weight": 1, "hecke_orbit": 3, "hecke_orbit_code": 9009260855823620, "dim": 12, "is_polredabs": true, "nf_label": "12.0.1157018619904.1", "trace_hash": 1787940231475956964, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [49, 0, -49, 0, 49, 0, 35, 0, 21, 0, 7, 0, 1]]], "qexp_display": "q-\\zeta_{28}^{8}q^{2}+(\\zeta_{28}^{7}+\\zeta_{28}^{13})q^{3}-\\zeta_{28}^{2}q^{4}+\\cdots", "char_order": 14, "char_parity": -1, "char_degree": 6, "char_conductor": 3332, "char_orbit_label": "be", "char_is_real": false, "Nk2": 3332, "analytic_conductor": 1.662884622093164, "hecke_ring_index": 1, "level_radical": 238, "projective_image": "D14", "projective_image_type": "Dn", "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 28, "field_poly_is_real_cyclotomic": false, "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": "0.762", "prec": 17}, "analytic_rank_proved": true, "char_values": [3332, 14, [1667, 885, 785], [7, 10, 7]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 8, "level_primes": [2, 7, 17], "conrey_indexes": [407, 1359, 1835, 2311, 2787, 3263], "field_disc": 1157018619904, "field_disc_factorization": [[2, 12], [7, 10]], "field_poly": [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.051", "prec": 17}, {"__RealLiteral__": 0, "data": "9.728", "prec": 17}, {"__RealLiteral__": 0, "data": "15.518", "prec": 20}, {"__RealLiteral__": 0, "data": "1008.623", "prec": 27}, {"__RealLiteral__": 0, "data": "7942.288", "prec": 27}, {"__RealLiteral__": 0, "data": "250801.556", "prec": 34}], "related_objects": [], "self_twist_discs": [-68], "cm_discs": [-68], "rm_discs": [], "relative_dim": 2, "trace_display": [2, 0, 0, 0], "traces": [0, 12, 2, 0, -2, 0, 0, 0, 2, -12, 0, 0, 0, -10, 0, 0, -2, -2, -16, 0, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 2, -14, 2, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -12, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -14, 0, 12, 14, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, -2, 4, 0, 0, -4, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 2, -10, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 10, 0, 0, 0, 0, 14, 0, 0, 0, -10, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 18, 0, 0, 14, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 14, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -14, -14, 0, 12, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 4, 14, 0, 0, 0, 12, 0, 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, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 4, 0, 0, 4, -2, -14, 0, 0, 14, 0, 0, 0, 4, 14, 0, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 4, 10, 0, 0, -4, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, -14, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, -4, 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, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 14, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, -4, 0, 0, 10, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 10, 0, 0, 0, 0, -14, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, -6, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, -14, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 10, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 14, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 10, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 10, 0, 0, 4, 2, 0, 0, 0, -14, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, -4, 14, 2, 0, -28, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 16, -4, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, -10, 10, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, -14, 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, -14, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, -10, 0, 0, 4, 0, 0, -2, 0, 0, 0, -24, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, -14, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 14, 0, 0, 0, -4, -4, 0, 0, 0, 14, 0, 0, 14, 0, 0, 0, 0, 4, 0, 0, 0, 14, -4, 0, 0, 0, 0, 0, 0, 0, 14, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 10, 0, -2, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -14, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 14, 0, 0, 0, -10, 0, -28, 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, 0, 0, 0, -16, 2, 4, 0, 0, 0, 0, 0, -14, -4, 0, 0, 0, 10, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 4, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -14, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 14, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, -2, 6, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, -14, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, -14, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 4, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, -4, 0, 0, 0, 0, 0, 0, -22, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 4, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, -2, 0, 0, 0, 14, 10, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, -4, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 10, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 14, 0, -2, 14, 0, 0, -14, 0, 0, 0, 0, -4, 0, 0, 0, 14, 0, 0, 0, -10, 0, 0, 0, -4, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, -4, 0, 14, 0, 0, 14, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 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, -4, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 4, 0, 0, 0, 0, 0, 0, 0, 0, 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, 10, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0], "projective_field": [316578250, 322896350, 234356465, 140041062, 35128268, -2471644, -1885569, -45292, 44394, 11774, 399, -378, 0, 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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 68, 4, -1, 2, -68], [1, 1, 4, 2, -1, 2, 0], [1, 1, 17, 2, 1, 2, 0], [1, 1, 49, 5, 1, 7, 0], [1, 1, 196, 11, -1, 14, 0], [1, 1, 833, 18, 1, 14, 0], [1, 1, 3332, 31, -1, 14, 0]], "char_orbit_index": 31, "prim_orbit_index": 31, "minimal_twist": "3332.1.be.c", "char_is_minimal": true, "conrey_index": 407, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "sato_tate_group": null, "atkin_lehner_eigenvals": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[], [[1, 0]], [[-1, 8]], [[1, 7], [1, 13]], [[-1, 2]], [], [[1, 1], [1, 7]], [[1, 3]], [[1, 10]], [[-1, 0], [-1, 6], [-1, 12]], [], [[1, 7], [1, 9]], [[1, 1], [-1, 9]], [[-1, 0], [1, 2]], [[-1, 11]], [], [[1, 4]], [[1, 12]], [[-1, 0], [-1, 6], [1, 8]], [], [], [[-1, 2], [1, 10]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 3], [-1, 9]], [[-1, 6]], [[1, 8], [-1, 10]], [[2, 5], [-1, 5], [-1, 7], [1, 11], [-1, 13]], [[-1, 5]], [], [], [[1, 3], [-1, 11]], [[-1, 12]], [[-1, 0], [-1, 2], [-1, 6], [-1, 8]], [[1, 6]], [], [[-1, 0], [1, 2], [1, 8]], [], [], [[-1, 1], [-1, 7], [1, 9], [-1, 13]], [], [], [[1, 4], [1, 10]], [], [[-1, 9], [-1, 11]], [], [[1, 9], [1, 11]], [], [[-1, 3], [1, 11]], [[1, 6]], [[-1, 0]], [[-1, 5], [-1, 11]], [[1, 2], [-1, 4]], [[-1, 6], [1, 12]], [[-1, 1], [1, 5], [-1, 7], [-1, 13]], [], [[1, 13]], [], [], [], [], [], [[-1, 5], [-1, 11]], [[1, 1], [-1, 3], [-1, 9]], [[-1, 6]], [], [[-1, 0], [-1, 2], [1, 8], [1, 10]], [], [[1, 0]], [[1, 0], [1, 2], [-1, 8], [-1, 10]], [], [[-1, 5], [1, 13]], [[1, 2], [1, 8], [-1, 10]], [], [], [[1, 5], [-1, 13]], [], [[1, 10], [1, 12]], [[-1, 1], [1, 3], [-1, 7], [1, 9]], [[-1, 1], [1, 13]], [], [[1, 0], [-2, 4], [1, 4], [1, 6], [-1, 10], [1, 12]], [], [], [[1, 4], [-1, 12]], [], [], [], [[-1, 3], [-1, 5]], [[1, 2], [1, 10]], [], [[-1, 3], [1, 5]], [[1, 3], [1, 5]], [[-1, 2], [1, 4], [1, 10], [1, 10]], [], [], [[1, 5], [1, 11]], [], [[1, 0]], [[1, 1], [1, 5], [-1, 7], [1, 7], [-1, 9], [-1, 13]], [[1, 8]]]}