# Stored data for newform 1400.1.bf.a, downloaded from the LMFDB on 19 April 2024.
{"label": "1400.1.bf.a", "space_label": "1400.1.bf", "level": 1400, "weight": 1, "hecke_orbit": 1, "hecke_orbit_code": 2130320557432, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 2192433335632095160, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[17, [3, -3, 1]]], "qexp_display": "q+\\zeta_{6}^{2}q^{2}-\\zeta_{6}q^{4}+\\zeta_{6}^{2}q^{7}+q^{8}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 56, "char_orbit_label": "bf", "char_is_real": false, "Nk2": 1400, "analytic_conductor": 0.6986910176862033, "hecke_ring_index": 1, "level_radical": 70, "projective_image": "D6", "projective_image_type": "Dn", "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "field_poly_is_real_cyclotomic": false, "projective_field_label": "6.0.5378240000.1", "hecke_ring_index_proved": true, "self_twist_type": 2, "is_self_dual": false, "is_self_twist": true, "is_cm": false, "is_rm": true, "trace_zratio": {"__RealLiteral__": 0, "data": "0.637", "prec": 17}, "analytic_rank_proved": true, "char_values": [1400, 6, [351, 701, 1177, 801], [6, 3, 6, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 4, "level_primes": [2, 5, 7], "conrey_indexes": [101, 901], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.025", "prec": 17}, {"__RealLiteral__": 0, "data": "2.014", "prec": 17}, {"__RealLiteral__": 0, "data": "0.119", "prec": 17}, {"__RealLiteral__": 0, "data": "18.053", "prec": 20}, {"__RealLiteral__": 0, "data": "-1.025", "prec": 20}, {"__RealLiteral__": 0, "data": "200.224", "prec": 24}], "related_objects": [], "self_twist_discs": [8], "cm_discs": [], "rm_discs": [8], "relative_dim": 1, "trace_display": [-1, 0, 0, -1], "traces": [0, 2, -1, 0, -1, 0, 0, -1, 2, 1, 0, 0, 0, 0, -1, 0, -1, 3, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 3, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, -3, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, -1, 0, -1, -3, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, -3, 0, 0, 0, 2, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -3, 0, -2, -4, -1, 0, 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 2, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 3, 0, -1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -3, -2, 0, 0, -1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, -3, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 3, 0, 0, 0, 0, -3, 0, 3, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -1, 3, 0, 0, -2, 0, -3, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -3, 0, 0, 0, 0, -3, 0, -2, 0, 0, 0, 0, 3, 0, -1, -2, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 1, 3, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, -3, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, -1, 0, 0, 0, 0, 3, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0, 0, -3, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 3, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, -2, -3, 0, 3, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, -3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -3, 0, 0, 6, 0, 3, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -3, 0, 0, 0, 1, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, -3, 0, 3, 0, 0, 0, 0, -3, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, -3, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -3, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, -4, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 2, 3, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 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, 0, 0, 1, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 2, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 3, 0, -3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, -2, -2, 0, 0, 0, 0, 0, -3, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, -1, 0, 0, 0, 0, -3, 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, 0, 0, 0, 0, 1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, -3, 0, -3, 0, 0, 0, 0, 0, 0, 3, 0, 0, 4, 0, 3, 1, 0, 0, 0, 0, 1, 0, 0, -3, 0, -2, 0, 0, 0, 0, 3, 0, 0, 6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, -3, 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, 6, 0, 0, 0, 0, 0, -3, 0, -1, -3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -3, 0, 3, 0, 0, 3, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 3, -3, 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, -4, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 2, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -6, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 4, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -3, 0, 2, 0, 0, 0, 0, 0, -2, 1, 0, 0, -3, 0, -1, 0, 0, -3, 2, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 3, 0, 0, 0, 2, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1, 0], "projective_field": [126, 0, 133, 0, 28, 0, 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, 8, 2, 1, 2, 8], [1, 1, 7, 4, -1, 6, 0], [1, 1, 56, 10, -1, 6, 0]], "char_orbit_index": 32, "prim_orbit_index": 10, "minimal_twist": "1400.1.bf.a", "char_is_minimal": true, "conrey_index": 101, "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, 2]], [], [[-1, 1]], [], [], [[1, 2]], [[1, 0]], [[-1, 2]], [], [], [], [], [[-1, 1]], [], [[1, 2]], [[1, 0], [-1, 2]], [[1, 1]], [], [], [], [], [[1, 2]], [], [], [], [], [[1, 0]], [], [], [[1, 0], [-1, 2]], [[-1, 1]], [], [[1, 1], [1, 2]], [], [[-1, 0]], [], [], [], [], [[1, 1], [1, 2]], [], [], [], [], [[-1, 1]], [[1, 0], [1, 1]], [], [[-1, 1]], [], [], [], [], [], [], [[1, 2]], [], [], [], [], [], [[1, 1], [1, 2]], [[1, 1]], [[1, 0]], [], [], [], [[-1, 0], [-1, 1]], [], [], [[1, 0]], [[-1, 2]], [], [], [], [], [], [], [[1, 2]], [], [[-1, 1]], [[-1, 0], [-1, 1]], [], [], [], [], [], [], [[1, 0], [1, 1]], [], [], [[1, 0]], [], [[-1, 0], [1, 2]], [], [], [[-1, 1], [-1, 2]], [[1, 0]], [], []]}