# Stored data for newform 975.2.bp.d, downloaded from the LMFDB on 25 April 2024.
{"label": "975.2.bp.d", "space_label": "975.2.bp", "level": 975, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13513616414213071, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 201049501855806895, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [0, 1]], [7, [169, -130, 41, -8, 1]]], "qexp_display": "q+(2-\\zeta_{12}^{2})q^{3}-2\\zeta_{12}q^{4}+(1-\\zeta_{12}+\\cdots)q^{7}+\\cdots", "char_order": 12, "char_parity": 1, "char_degree": 4, "char_conductor": 195, "char_orbit_label": "bp", "char_is_real": false, "Nk2": 3900, "analytic_conductor": 7.785414197074838, "hecke_ring_index": 1, "level_radical": 195, "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": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.656", "prec": 17}, "analytic_rank_proved": true, "char_values": [975, 12, [326, 352, 301], [6, 6, 5]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [3, 5, 13], "conrey_indexes": [149, 449, 674, 899], "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": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.745", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "85.229", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2933.268", "prec": 27}], "related_objects": [], "self_twist_discs": [-3], "cm_discs": [-3], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.1.d12", "trace_display": [0, 6, 0, 8], "traces": [0, 4, 0, 6, 0, 0, 0, 8, 0, 6, 0, 0, 0, 10, 0, 0, 8, 0, 0, -14, 0, 18, 0, 0, 0, 0, 0, 0, 16, 0, 0, -14, 0, 0, 0, 0, 0, 22, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 24, -18, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 30, 0, 0, 0, 10, 0, 0, 0, 0, 0, 34, 0, 0, -28, 0, 0, 0, 0, -18, 0, 0, 12, 0, 0, 0, 0, 0, 0, 2, 0, -36, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -38, 0, 42, -8, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, -16, 0, 0, -2, 0, 0, 0, 0, 0, -66, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 48, 0, 0, -18, -40, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34, 0, 0, 0, 0, 0, -2, 0, 6, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 4, 0, 0, 56, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 54, 0, 0, 0, -10, 0, 0, 0, 0, -60, -44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -62, 0, -54, 60, 0, 0, -62, 0, 0, 0, 0, -12, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, -2, 0, 36, 0, 0, 0, 0, 0, -66, 0, 0, 0, -50, 0, 0, 0, 0, 0, -34, 0, -66, -28, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, -64, 0, 0, 70, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -42, 0, 0, 0, -64, 0, 60, 0, 0, 24, 116, 0, 0, 0, 0, 0, -54, 0, 0, 0, 0, 0, 28, 0, 54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 76, 0, 0, 0, 0, 0, 0, 0, -60, 126, 0, 0, 0, 0, 0, -58, 0, -6, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, -70, 0, -66, 0, 0, 0, 10, 0, 0, 0, 0, 0, -14, 0, 0, 108, 0, 0, 0, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 72, 70, 0, 0, 68, 0, 0, 138, 0, 0, 0, 0, -84, 0, 0, 0, 80, 0, 0, 0, 0, 30, 0, 0, 0, 62, 0, 0, 0, 0, 0, 86, 0, 0, 0, 0, 0, 148, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 44, 0, 0, 50, 0, -18, 0, 0, 0, 0, 0, 0, 32, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, 150, 0, 54, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -46, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, -34, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92, 0, -42, 0, 0, 0, 0, 0, 0, 0, 0, 84, 162, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -66, -92, 0, 0, 0, 0, 0, 0, 0, 0, 94, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 24, 0, 0, 0, 44, 0, 0, -88, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, -96, -68, 0, 0, 0, 0, 60, 0, 0, 0, 76, 0, 0, 0, 0, 0, 0, 0, -66, 0, 0, 0, 0, 0, 0, 0, 0, 0, -94, 0, 0, 0, 0, -96, 0, 0, -30, 0, 0, 0, -98, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 62, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54, 0, -96, 0, 0, 0, -196, 0, -108, 0, 0, 60, -14, 0, 0, 0, 0, 0, 106, 0, -102, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, -72, -168, 0, 0, 0, 0, 0, -186, 0, 0, 0, 0, 0, 98, 0, 0, 92, 0, 0, 0, 0, 102, 0, 0, 0, 0, 0, 0, -72, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 0, 68, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 38, 0, -60, 0, 0, 0, 18, 0, 102, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -90, 0, 0, 0, -58, 0, 0, 0, 0, 0, 88, 0, -150, 0, 0, 0, -70, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -102, -76, 0, 0, 106, 0, -114, 0, 0, 12, 50, 0, 0, 0, 0, 0, -220, 0, 0, 0, 0, 0, 2, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, -80, 0, 0, 0, 0, -120, 0, 0, 0, -116, 0, 0, 0, 0, 102, 0, 0, 0, 0, 0, 0, 0, 0, 0, -76, 0, 0, 0, 0, 0, 0, 0, 114, 0, 0, 0, 0, 0, 0, 0, 0, -168, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 124, 0, 0, 40, 0, 0, 0, 0, 0, -70, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, -16, 0, 0, -88, 0, -66, 0, 0, 0, 0, 0, 54, 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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 65, 19, -1, 12, 0], [1, 1, 195, 34, 1, 12, 0]], "char_orbit_index": 42, "prim_orbit_index": 34, "minimal_twist": "39.2.k.a", "char_is_minimal": false, "conrey_index": 149, "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, 0, 0, 0], [2, 0, -1, 0], [0, -2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [1, -1, 2, 3], [0, 0, 0, 0], [3, 0, -3, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -4, 0, 2], [1, 0, 3, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 4, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-5, 5, 3, -2], [0, 0, 0, 0], [4, 1, 1, 4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [3, 0, -6, 0], [6, -2, -4, -4], [0, 0, 0, 0], [0, 0, 0, 0], [-1, 5, -5, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -6, 0, 6], [4, 7, 3, -3], [0, 0, 0, 0], [5, 0, 2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [4, 0, 4, 0], [-6, -7, 3, 7], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2, 0, -6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-7, 8, 8, -7], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -5, 0, 10], [0, 0, 0, 0], [9, 6, -3, 3], [0, 0, 0, -8], [0, 0, 0, 0], [0, 0, 0, 0], [7, 2, -9, -9], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [8, -1, 1, -8], [0, 0, 0, 0], [0, 0, 0, 0], [-4, 10, -6, -6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 14, 0, -7], [0, 0, 0, 0], [0, 0, -9, 0], [0, 0, 0, 0], [0, 0, 0, 0], [8, -8, -10, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-5, -10, 11, 9], [0, 0, 0, 0], [-7, 11, -4, -4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-3, -3, -8, 11], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}