# Stored data for newform 2500.1.j.c, downloaded from the LMFDB on 23 April 2024. {"label": "2500.1.j.c", "space_label": "2500.1.j", "level": 2500, "weight": 1, "hecke_orbit": 3, "hecke_orbit_code": 9007817746811332, "dim": 8, "is_polredabs": true, "nf_label": "8.0.4000000.1", "trace_hash": 339514815147740106, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [1, 0, 1, 0, 6, 0, -4, 0, 1]], [13, [0, 1]]], "qexp_display": "q-\\zeta_{20}q^{2}+(\\zeta_{20}-\\zeta_{20}^{3})q^{3}+\\zeta_{20}^{2}q^{4}+\\cdots", "char_order": 10, "char_parity": -1, "char_degree": 4, "char_conductor": 100, "char_orbit_label": "j", "char_is_real": false, "Nk2": 2500, "analytic_conductor": 1.247662531582506, "hecke_ring_index": 1, "level_radical": 10, "projective_image": "D5", "projective_image_type": "Dn", "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 20, "field_poly_is_real_cyclotomic": false, "projective_field_label": "5.1.250000.1", "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": "0.760", "prec": 17}, "analytic_rank_proved": true, "char_values": [2500, 10, [1251, 1877], [5, 8]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 8, "level_primes": [2, 5], "conrey_indexes": [251, 751, 1751, 2251], "field_disc": 4000000, "field_disc_factorization": [[2, 8], [5, 6]], "field_poly": [1, 0, -1, 0, 1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "-0.064", "prec": 20}, {"__RealLiteral__": 0, "data": "7.560", "prec": 17}, {"__RealLiteral__": 0, "data": "-5.346", "prec": 20}, {"__RealLiteral__": 0, "data": "716.996", "prec": 24}, {"__RealLiteral__": 0, "data": "-1062.817", "prec": 30}, {"__RealLiteral__": 0, "data": "151266.802", "prec": 34}], "related_objects": [], "self_twist_discs": [-20], "cm_discs": [-20], "rm_discs": [], "relative_dim": 2, "trace_display": [0, 0, 0, 0], "traces": [0, 8, 0, 0, 2, 0, -4, 0, 0, 6, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 6, 0, 0, 0, 0, 6, 0, 0, -4, 0, 0, 0, 0, -2, 0, 6, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 6, 0, 0, 4, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, -2, 0, 0, 0, 0, 8, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -8, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -6, 0, -4, 0, 0, 2, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, -8, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -6, 0, 2, 0, 0, 8, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, -6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, -6, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -6, 0, 2, 0, 0, 4, 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, 6, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, -16, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, -4, 0, 0, -6, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 6, 0, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, -4, 0, 0, 4, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 6, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -6, 0, 2, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 4, 0, -4, 0, 0, 4, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, -4, 0, 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, -16, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, -2, 0, 0, 8, 0, 0, 0, 0, 8, 0, -4, 0, 0, 0, 0, -6, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, -2, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, -6, 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, -2, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, -2, 0, 0, 8, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, -6, 0, 0, 0, 0, -6, 0, 6, 0, 0, 0, 0, -4, 0, 0, -8, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 2, 0, 0, 0, 0, -8, 0, 0, 6, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, -8, 0, 0, -2, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 16, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -16, 0, 8, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 8, 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, 12, 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, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 8, 0, -4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 6, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 6, 0, 0, 2, 0, 0, 0, 0, 8, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -8, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 6, 0, 0, 0, 0, -4, 0, 0, -6, 0, 0, 0, 0, 2, 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, 4, 0, 0, -12, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, -6, 0, 0, -2, 0, 0, 0, 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, -4, 0, 0, -6, 0, 0, 0, 0, 4, 0, 0, 0, 0, -12, 0, -4, 0, 0, 0, 0, 6, 0, 0, 8, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -6, 0, 2, 0, 0, -12, 0, 0, 0, 0, -6, 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, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, -2, 0, -4, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 16, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -6, 0, 0, 0, 0, -4, 0, 0, 0, 0, -8, 0, -4, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, -2, 0, 0, 0, 0, -6, 0, -2, 0, 0, 0, 0, 12, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], "projective_field": [-4, 10, 0, -5, 0, 1], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 20, 4, -1, 2, -20], [1, 1, 4, 2, -1, 2, 0], [1, 1, 5, 2, 1, 2, 0], [1, 1, 25, 4, 1, 5, 0], [1, 1, 25, 5, 1, 10, 0], [1, 1, 100, 8, -1, 10, 0], [1, 1, 100, 10, -1, 10, 0]], "char_orbit_index": 10, "prim_orbit_index": 10, "minimal_twist": "500.1.b.a", "char_is_minimal": false, "conrey_index": 251, "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, 1]], [[1, 1], [-1, 3]], [[1, 2]], [], [[-1, 2], [1, 4]], [[1, 3], [1, 7]], [[-1, 3]], [[1, 2], [-1, 4], [1, 6]], [], [], [[1, 3], [-1, 5]], [], [[-1, 4], [-1, 8]], [], [[1, 4]], [], [[-1, 3], [1, 5], [-1, 7]], [], [], [[1, 0], [1, 4], [-1, 6], [1, 8]], [], [[-1, 3], [1, 9]], [[-1, 4], [1, 6]], [], [], [[1, 3], [-1, 5], [1, 7], [-1, 9]], [[1, 5], [1, 9]], [[1, 6], [-1, 8]], [], [], [[-1, 5]], [], [], [], [[1, 4], [-1, 6], [1, 8]], [], [], [], [], [[1, 0], [1, 8]], [[-1, 1], [-1, 5], [1, 7], [-1, 9]], [[1, 1], [1, 9]], [], [], [[1, 0], [1, 4]], [[-1, 1], [1, 3]], [[1, 5], [-1, 7]], [[-1, 0], [-1, 4], [1, 6]], [], [], [], [], [[-1, 0], [-1, 4], [1, 6], [-1, 8]], [], [[1, 0], [-1, 6]], [], [[-1, 7], [1, 9]], [], [], [[1, 4], [1, 8]], [], [[1, 1], [-1, 3], [1, 5], [-1, 7], [2, 9]], [[1, 6]], [], [], [[1, 3], [1, 3]], [], [[-1, 0], [1, 2], [-1, 4], [1, 6]], [], [], [[-1, 5], [1, 7], [-1, 9]], [], [], [], [], [], [], [], [], [[2, 0], [-1, 0], [-1, 2], [1, 4], [-1, 6], [1, 8]], [[-1, 1], [-1, 9]], [[1, 1], [1, 5]], [[-1, 0], [1, 2], [1, 6], [-1, 8]], [], [[1, 0], [-1, 2]], [[-1, 1], [1, 7], [-2, 9]], [], [[-1, 4], [-1, 8]], [], [], [[-1, 1], [-1, 5]], [], [[1, 2], [-1, 4]], [], [[-1, 6], [1, 8]], [], [[1, 1], [1, 5], [-1, 7]], [], []]}