# Stored data for newform 3332.1.bp.d, downloaded from the LMFDB on 23 April 2024.
{"label": "3332.1.bp.d", "space_label": "3332.1.bp", "level": 3332, "weight": 1, "hecke_orbit": 4, "hecke_orbit_code": 13513616397438212, "dim": 8, "is_polredabs": true, "nf_label": "8.0.5308416.1", "trace_hash": 2157756333773526854, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [4, -8, 4, -8, 18, -16, 10, -4, 1]]], "qexp_display": "q+\\zeta_{24}^{7}q^{2}-\\zeta_{24}^{2}q^{4}+(-\\zeta_{24}+\\zeta_{24}^{4}+\\cdots)q^{5}+\\cdots", "char_order": 24, "char_parity": -1, "char_degree": 8, "char_conductor": 476, "char_orbit_label": "bp", "char_is_real": false, "Nk2": 3332, "analytic_conductor": 1.662884622093164, "hecke_ring_index": 1, "level_radical": 238, "projective_image": "D8", "projective_image_type": "Dn", "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 24, "field_poly_is_real_cyclotomic": false, "projective_field_label": "8.2.3089659810545728.1", "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": "0.791", "prec": 17}, "analytic_rank_proved": true, "char_values": [3332, 24, [1667, 885, 785], [12, 16, 15]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 8, "level_primes": [2, 7, 17], "conrey_indexes": [263, 655, 1243, 1647, 2235, 2627, 3007, 3215], "field_disc": 5308416, "field_disc_factorization": [[2, 16], [3, 4]], "field_poly": [1, 0, 0, 0, -1, 0, 0, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.016", "prec": 17}, {"__RealLiteral__": 0, "data": "7.875", "prec": 17}, {"__RealLiteral__": 0, "data": "-4.981", "prec": 20}, {"__RealLiteral__": 0, "data": "640.000", "prec": 24}, {"__RealLiteral__": 0, "data": "-1131.580", "prec": 30}, {"__RealLiteral__": 0, "data": "100511.377", "prec": 34}], "related_objects": [], "self_twist_discs": [-4], "cm_discs": [-4], "rm_discs": [], "relative_dim": 1, "trace_display": [0, 0, 4, 0], "traces": [0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, -8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, -8, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, -24, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 8, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, -8, 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, 4, 0, 0, 4, 0, 0, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, -4, 0, 0, -16, -4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 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, -8, 0, 0, -4, 0, 0, 0, 0, 0, 0, -4, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -8, 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, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 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, 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, -4, 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, 8, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -16, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, 0, 8, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, -4, 0, 0, 0, 0, 8, 0, -4, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 8, 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, -8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, -8, 4, 0, 0, -12, 0, 0, 8, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 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, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, -8, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -4, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 8, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -8, 0, 0, 0, 0, -16, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -8, 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, 8, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 8, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -8, 0, -8, 0, 0, 4, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -8, -8, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, -8, 0, 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, 4, 0, 0, 0, 4, 0, 0, 0, 8, 0, -8, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, -8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -4, 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, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 4, 0, 0, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 0, 16, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -4, 0, 0, 4, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 0, -4, 0, 0, -8, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 8, 0, 0, 8, -8, 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, -4, 0, 0, 0, -8, 0, -4, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 8, 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, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -16, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 4, 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, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4], "projective_field": [-2736, 240, -776, 292, -287, -54, -62, -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, 4, 1, 8, 0], [1, 1, 28, 7, -1, 6, 0], [1, 1, 68, 7, -1, 8, 0], [1, 1, 119, 17, 1, 24, 0], [1, 1, 476, 33, -1, 24, 0]], "char_orbit_index": 42, "prim_orbit_index": 33, "minimal_twist": "3332.1.w.a", "char_is_minimal": false, "conrey_index": 263, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "sato_tate_group": null, "atkin_lehner_eigenvals": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[], [[1, 0]], [[1, 7]], [], [[-1, 2]], [[-1, 1], [1, 4]], [], [], [[-1, 9]], [[-1, 1]], [[-1, 8], [1, 11]], [], [], [[-1, 6], [-1, 6]], [], [], [[1, 4]], [[1, 5]], [[-1, 8]], [], [[1, 3], [-1, 6]], [], [], [], [], [[1, 2], [-1, 5], [1, 8]], [[2, 1]], [], [], [[1, 3], [1, 6]], [], [], [[1, 11]], [], [[-1, 0]], [], [[1, 3]], [[1, 1], [1, 4]], [], [], [[1, 1], [1, 10]], [[1, 6], [1, 9]], [], [], [], [[1, 2], [-1, 5]], [], [], [], [], [[1, 0], [-1, 3], [1, 9]], [], [[2, 8]], [[1, 2], [-1, 8]], [], [], [], [], [[-1, 1], [1, 10]], [], [], [[-1, 1], [1, 10]], [], [], [[-1, 6]], [[2, 7], [-2, 10]], [], [], [[-1, 7]], [], [], [], [[1, 10]], [[1, 5], [-1, 8]], [[1, 8], [1, 11]], [], [], [], [], [], [[-1, 5], [1, 8]], [[1, 2]], [[-1, 1], [-1, 4]], [], [], [[-1, 6], [1, 9]], [], [], [], [], [[1, 0], [1, 9]], [], [], [], [], [], [], [[-1, 0], [-1, 9]], [], [], [[-1, 4], [1, 7], [-1, 10]]]}