# Stored data for newform 791.1.x.a, downloaded from the LMFDB on 24 April 2024.
{"label": "791.1.x.a", "space_label": "791.1.x", "level": 791, "weight": 1, "hecke_orbit": 1, "hecke_orbit_code": 1580564742935, "dim": 12, "is_polredabs": true, "nf_label": "12.0.1157018619904.1", "trace_hash": 628163653530908012, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+(-\\zeta_{28}^{3}+\\zeta_{28}^{7})q^{2}+(-1+\\zeta_{28}^{6}+\\cdots)q^{4}+\\cdots", "char_order": 28, "char_parity": -1, "char_degree": 12, "char_conductor": 791, "char_orbit_label": "x", "char_is_real": false, "Nk2": 791, "analytic_conductor": 0.3947604249927049, "hecke_ring_index": 1, "level_radical": 791, "projective_image": "D28", "projective_image_type": "Dn", "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 28, "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": "0.665", "prec": 17}, "analytic_rank_proved": true, "char_values": [791, 28, [227, 568], [14, 17]], "hecke_ring_generator_nbound": 9, "inner_twist_count": 4, "level_primes": [7, 113], "conrey_indexes": [111, 258, 279, 286, 307, 454, 573, 622, 664, 692, 734, 783], "field_disc": 1157018619904, "field_disc_factorization": [[2, 12], [7, 10]], "field_poly": [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "-0.068", "prec": 20}, {"__RealLiteral__": 0, "data": "11.249", "prec": 20}, {"__RealLiteral__": 0, "data": "-6.389", "prec": 20}, {"__RealLiteral__": 0, "data": "1494.521", "prec": 27}, {"__RealLiteral__": 0, "data": "-698.677", "prec": 27}, {"__RealLiteral__": 0, "data": "237516.638", "prec": 34}], "related_objects": [], "self_twist_discs": [-7], "cm_discs": [-7], "rm_discs": [], "relative_dim": 1, "trace_display": [0, 0, 0, -2], "traces": [0, 12, 0, 0, -12, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -12, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 14, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 12, -2, 0, 0, 16, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -16, 0, 0, 0, 14, 0, 0, 2, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 2, -12, 14, 0, 14, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, -14, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, -2, 0, 0, 12, 0, 2, 0, -12, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 14, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 14, 0, 0, 0, 0, -16, 0, -14, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 4, 0, -12, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 12, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 12, 0, 0, 2, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 2, 0, 0, 0, -14, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 16, 0, 0, -12, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, -14, 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, 0, 0, 0, 0, 0, -14, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 14, 4, 0, -2, 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, -2, 0, 0, -14, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, -14, -2, 0, 2, 0, 0, 2, 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, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -28, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -2, 14, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 12, 0, 0, -2, -28, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -14, 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, -14, 0, 0, 0, 0, 12, 4, 0, 0, 10, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, -2, 0, 0, 0, 0, 14, 2, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, -14, 2, 0, 0, 0, 0, 0, -4, 14, 0, 0, 0, 0, 12, 0, 2, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 2, 0, 0, 0, 0, 0, 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, -4, 0, 0, 14, 0, 0, 0, -28, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, -2, 12, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, -14, 0, 0, 0, 0, 0, 0, 12, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 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, 2, 14, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, -14, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -14, 0, 0, 4, 0, 0, -14, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 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, -14, 0, 0, 0, 0, 0, 14, 12, 0, 0, 0, 0, -14, 2, 0, 0, 0, 0, 0, 0, 16, -2, 0, 0, 0, 0, 0, -4, 14, 0, 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, 16, 0, -14, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 14, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -24, 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, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, -12, 0, 14, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 12, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 14, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 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, 14, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 14, 2, 0, -12, 0, 0, 14, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, -12, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, -4, 12, 0, 14, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 12, 0, 0, 0, -12, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 14, 0, 0, 0, 0, -14, 0, 0, 0, 0, 2, -12, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 16, 0, 0, 14, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 14, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 14, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, -10, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, -16, -2, 0, 12, 0], "projective_field": [-5542807101867, 32014633536459, -136518646923477, -171358022846871, 194440485026970, 87344373009201, -157717802038814, 14362429403516, 51018498763434, -20889289897159, -2481011680298, 3447049634172, -692687755424, -148581039871, 108996732546, -19261175383, -2694312125, 2056338753, -410559800, 4339526, 17365491, -4416817, 458335, 9996, -8084, 755, 27, -13, 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": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, -7], [1, 1, 113, 8, 1, 28, 0], [1, 1, 791, 24, -1, 28, 0]], "char_orbit_index": 24, "prim_orbit_index": 24, "minimal_twist": "791.1.x.a", "char_is_minimal": true, "conrey_index": 111, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "sato_tate_group": null, "atkin_lehner_eigenvals": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[], [[1, 0]], [[-1, 3], [1, 7]], [], [[-1, 0], [1, 6], [-1, 10]], [], [], [[1, 8]], [[2, 3], [-1, 3], [-1, 7], [-1, 9], [1, 13]], [[-1, 9]], [], [[-1, 10], [-1, 12]], [], [], [[-1, 1], [-1, 11]], [], [[1, 0], [2, 2], [-1, 2], [-2, 6], [1, 6], [1, 10], [1, 12]], [], [[1, 2], [1, 12]], [], [], [], [[-1, 1], [1, 3], [1, 5], [1, 13]], [[1, 8], [1, 11]], [], [[1, 5]], [], [], [[-1, 0], [1, 4], [-1, 8]], [[1, 4], [-1, 13]], [], [], [[1, 1], [-2, 3], [1, 3], [-2, 5], [1, 5], [1, 7], [2, 9], [-1, 9], [-1, 13]], [], [], [], [[1, 1], [-1, 5], [1, 9]], [[-1, 6], [1, 9]], [], [], [], [], [], [[-1, 4], [-1, 13]], [[1, 2], [1, 4], [-1, 6], [-1, 8], [1, 10], [1, 12]], [], [[1, 0], [-1, 1], [-1, 4], [-1, 11]], [], [], [[-1, 2]], [[-1, 8], [1, 12]], [], [], [[-1, 8], [-1, 12]], [], [], [[1, 1], [1, 3], [-1, 7], [1, 11]], [], [[-1, 2], [1, 6], [-1, 7], [1, 11]], [], [], [], [], [[1, 3]], [[-1, 0], [-2, 2], [1, 2], [-1, 4], [2, 6], [-1, 6], [2, 8], [-1, 8], [-1, 10], [-1, 12]], [], [], [[1, 2], [1, 13]], [], [], [], [[1, 10], [-1, 11]], [[-1, 2], [-1, 4], [1, 8], [-1, 12]], [], [[-1, 2], [1, 9], [-1, 12], [-1, 13]], [], [], [[1, 4], [1, 6]], [], [[-1, 3], [1, 10]], [], [[-1, 4]], [], [], [], [], [[-1, 2], [1, 6], [1, 7], [-1, 11]], [], [[1, 1], [-1, 3], [-2, 5], [-1, 7], [1, 9], [1, 11], [-1, 13]], [], [], [], [[-1, 0], [-1, 3], [1, 4], [1, 7], [-1, 8], [-1, 11]], [], [], [], [], [], [[1, 5], [-1, 9]], [[-1, 5], [-1, 7]], [[1, 1], [-1, 5], [1, 11]]]}