# Stored data for newform 3724.1.n.a, downloaded from the LMFDB on 20 April 2024. {"label": "3724.1.n.a", "space_label": "3724.1.n", "level": 3724, "weight": 1, "hecke_orbit": 1, "hecke_orbit_code": 893369978508, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [], "qexp_display": "q+\\zeta_{12}q^{2}+\\zeta_{12}^{3}q^{3}+\\zeta_{12}^{2}q^{4}+\\zeta_{12}^{4}q^{6}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 532, "char_orbit_label": "n", "char_is_real": false, "Nk2": 3724, "analytic_conductor": 1.858518107045301, "hecke_ring_index": 1, "level_radical": 266, "projective_image": "A4", "projective_image_type": "A4", "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 12, "field_poly_is_real_cyclotomic": false, "projective_field_label": "4.0.283024.1", "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [3724, 6, [1863, 3041, 3137], [3, 4, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 4, "level_primes": [2, 7, 19], "conrey_indexes": [1831, 2823], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 4, 0, 0, 0, 0, -2, 0, -4, 2, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, -2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, -2, 0, 0, 0, -4, -2, 0, -4, 0, 0, 0, 2, 4, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, -4, 0, 2, 4, 0, 0, 0, 2, 2, 0, -2, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 2, 0, -4, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, -2, 0, 0, 0, 2, 4, 0, -4, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0, 2, 0, 0, 0, 0, -2, 2, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 2, 2, -2, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 8, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 4, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, -2, -4, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, -8, 0, 0, 4, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, -2, -2, 0, 4, -2, 0, 0, 0, -2, -4, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, -4, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, -2, 2, 0, 0, -2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 2, -2, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, -4, -2, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, -2, 0, 2, 2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, -4, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 4, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, -2, 0, 0, 2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 2, -2, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, -4, 8, 0, -2, 4, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, -2, 0, 0, 2, -4, 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, -4, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, -2, 0, 0, 2, 0, 0, 0, 2, 4, 0, 0, -4, 0, 0, 0, -2, 4, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -2, 0, 0, 0, 2, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 2, 2, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 2, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -4, 4, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 2, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, -2, -2, 0, 0, 4, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 4, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, -4, 0, -2, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, -2, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 4, 4, 0, 0, -4, 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, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0, 0, -2, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, -2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 4, 2, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, -4, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, -4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, 2, 0, 0, -2, -2, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 2, -4, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 4, 0, 2, -2, 0, 0, 2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 4, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -4, -2, 0, 0, -2, 2, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, 2, 0, 4, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, -8, 0, 0, -2, 0, 0, 0, -2, 2, 0, 0, -4, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, -2, 0, -2, 0, -2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, -4, -4, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 8, 2, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 2, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, -2, 0, 0, 0, -2, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, -2, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 8, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, -2, -4, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, -4, -2, 0, 0, -2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0], "projective_field": [6, 2, 7, -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, 0], [1, 1, 133, 7, 1, 3, 0], [1, 1, 532, 14, -1, 6, 0]], "char_orbit_index": 14, "prim_orbit_index": 14, "minimal_twist": "532.1.n.a", "char_is_minimal": false, "conrey_index": 1831, "id": null, "trace_hash": null, "fricke_eigenval": null, "atkin_lehner_string": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "trace_zratio": null, "trace_moments": null, "sato_tate_group": null, "atkin_lehner_eigenvals": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[], [[1, 0]], [[1, 1]], [[1, 3]], [[1, 2]], [], [[1, 4]], [], [[1, 3]], [], [], [[-1, 1]], [[1, 5]], [[1, 4]], [], [], [[1, 4]], [[1, 0]], [], [[1, 1]], [], [], [[-1, 2]], [[-1, 3]], [[-1, 0]], [[1, 2]], [[1, 5]], [[1, 3]], [], [[1, 4]], [], [[-1, 1]], [[1, 5]], [[-1, 4]], [[1, 1]], [], [], [[-1, 2]], [[1, 2]], [[-1, 1]], [], [[1, 2]], [], [[1, 5]], [[-1, 3]], [], [[-1, 4]], [[-1, 3]], [[-1, 1]], [], [[1, 3]], [[1, 3]], [[-1, 0]], [], [[1, 4]], [], [], [[1, 4]], [[1, 5]], [[-1, 3]], [], [[-1, 0]], [[-1, 2]], [], [[-1, 0]], [], [[-1, 5]], [], [[1, 2]], [[1, 0]], [], [[-1, 5]], [], [[1, 0]], [[-1, 3]], [[1, 5]], [[1, 3]], [], [[-1, 2]], [], [], [[-1, 0]], [[1, 3]], [], [], [], [[-1, 0]], [[-1, 1]], [[-1, 4]], [[1, 0]], [], [], [[-1, 5]], [[-1, 4]], [[-1, 4]], [], [[-1, 2]], [[-1, 2]], [], [], [[1, 4]]]}