# Stored data for newform 3025.1.bq.a, downloaded from the LMFDB on 16 September 2025. {"Nk2": 3025, "analytic_conductor": 1.5096716632148321, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 275, "char_degree": 8, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 43, "char_orbit_label": "bq", "char_order": 20, "char_parity": -1, "char_values": [3025, 20, [727, 2301], [7, 16]], "cm_discs": [-11], "conrey_index": 3, "dim": 8, "field_disc": 4000000, "field_disc_factorization": [[2, 8], [5, 6]], "field_poly": [1, 0, -1, 0, 1, 0, -1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 20, "has_non_self_twist": 1, "hecke_cutters": [], "hecke_orbit": 1, "hecke_orbit_code": 2886234803153, "hecke_ring_generator_nbound": 4, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 11, 2, -1, 2, -11], [1, 1, 275, 33, 1, 20, 0], [1, 1, 275, 42, -1, 20, 0]], "is_cm": true, "is_largest": true, "is_maximal": true, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": true, "is_twist_minimal": true, "label": "3025.1.bq.a", "level": 3025, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [5, 11], "level_radical": 55, "minimal_twist": "3025.1.bj.a", "nf_label": "8.0.4000000.1", "prim_orbit_index": 42, "projective_field": [-880, 0, 2500, 0, -3375, 0, 1950, 0, -475, 0, -790, 0, -100, 0, 150, 0, 5, 0, -10, 0, 1], "projective_image": "D20", "projective_image_type": "Dn", "qexp_display": "q+(-\\zeta_{20}^{2}-\\zeta_{20}^{5})q^{3}+\\zeta_{20}^{3}q^{4}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "self_twist_discs": [-11], "self_twist_type": 1, "space_label": "3025.1.bq", "trace_display": [0, -2, 0, 0], "trace_hash": 2065273967153804857, "trace_moments": [{"__RealLiteral__": 0, "data": "0.016", "prec": 17}, {"__RealLiteral__": 0, "data": "7.673", "prec": 17}, {"__RealLiteral__": 0, "data": "-3.580", "prec": 20}, {"__RealLiteral__": 0, "data": "607.813", "prec": 24}, {"__RealLiteral__": 0, "data": "-1062.475", "prec": 30}, {"__RealLiteral__": 0, "data": "81345.494", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.667", "prec": 17}, "traces": [0, 8, 0, -2, 0, 0, 0, 0, 0, -10, 0, 0, 2, 0, 0, -2, 2, 0, 0, 0, 8, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -10, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -6, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, -10, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 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, -10, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, -8, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, -2, 6, 0, 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, 2, 0, 0, 8, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, -2, 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, -2, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 4, 0, -2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 8, 0, 0, 0, -10, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, -10, 6, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, -8, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 2, 0, 0, 0, 0, 0, 0, -2, 0, -10, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 4, 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, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, -2, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -10, 0, 0, 0, -2, 0, 0, -8, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, -10, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, -2, 0, 0, 0, 0, 0, 0, -2, 0, 8, 0, -10, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 4, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -8, 0, -10, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, -2, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 2, 0, 0, 0, -6, 0, 0, 10, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 8, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 6, 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, 0, 0, -2, 0, -12, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 10, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, -10, 0, 0, 0, 0, 2, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, -2, 0, 0, 0, 8, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -10, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 4, 0, 0, 0, -8, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 6, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 10, 0, 0, 0, 0, 0, 0, 0, 2, 0, 10, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 8, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, -4, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 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, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 6, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 2, 0, 0, -10, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 8, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 12, 2, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 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, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 6, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -6, 0, 2, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, -4, 0, 0, 0, 10, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 10, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -10, 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, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, -4, 0, 0, -10, 0, 0, -8, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 8, 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, 2, -2, 0, 0, 0, 0, 0, 0, -2, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], "weight": 1, "weight_parity": -1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field_label": null, "sato_tate_group": null, "qexp": [[], [[1, 0]], [], [[-1, 2], [-1, 5]], [[1, 3]], [[-1, 7]], [], [], [], [[-1, 0], [1, 4], [1, 7]], [], [], [[-1, 5], [-1, 8]], [], [], [[-1, 2], [1, 9]], [[1, 6]], [], [], [], [[1, 0]], [], [], [[-1, 3], [-1, 4]], [], [[-1, 4]], [], [[2, 2], [-1, 2], [1, 5], [-1, 6], [-1, 9]], [], [], [], [[-1, 5], [-1, 7]], [], [], [], [], [[-1, 0], [-1, 3], [1, 7]], [[-1, 0], [-1, 5]], [], [], [], [], [], [], [], [[1, 1], [1, 4], [1, 7]], [], [[1, 1], [-1, 6]], [[1, 1], [-1, 8]], [[1, 7]], [], [], [], [[1, 1], [-1, 4]], [], [], [], [], [], [[-1, 4], [-1, 6]], [[-1, 2], [-1, 5]], [], [], [], [[1, 9]], [], [], [[1, 5], [-1, 6]], [], [[1, 5], [1, 6], [1, 8], [1, 9]], [], [[1, 0], [1, 8]], [], [], [], [[1, 6], [1, 9]], [], [], [], [], [[1, 3]], [[1, 0], [-2, 1], [1, 1], [-2, 4], [1, 4], [-1, 7], [1, 8]], [], [], [], [], [], [], [], [[1, 3], [-1, 9]], [], [], [[-1, 6], [-1, 7]], [[-1, 0], [-1, 2], [1, 7], [1, 9]], [], [], [], [[1, 6], [-1, 9]], [], [], [[-1, 7]]]}