# Stored data for newform 1191.1.bb.a, downloaded from the LMFDB on 20 April 2024.
{"label": "1191.1.bb.a", "space_label": "1191.1.bb", "level": 1191, "weight": 1, "hecke_orbit": 1, "hecke_orbit_code": 1855442650279, "dim": 20, "is_polredabs": true, "nf_label": "20.0.328307557444402776721569.1", "trace_hash": 1602692137741287010, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q-\\zeta_{66}^{17}q^{3}+\\zeta_{66}^{24}q^{4}-\\zeta_{66}^{32}q^{7}+\\cdots", "char_order": 66, "char_parity": -1, "char_degree": 20, "char_conductor": 1191, "char_orbit_label": "bb", "char_is_real": false, "Nk2": 1191, "analytic_conductor": 0.5943864300459059, "hecke_ring_index": 1, "level_radical": 1191, "projective_image": "D33", "projective_image_type": "Dn", "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 33, "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": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [1191, 66, [398, 799], [33, 64]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 4, "level_primes": [3, 397], "conrey_indexes": [110, 140, 206, 260, 314, 332, 503, 548, 569, 587, 764, 767, 902, 914, 941, 965, 1028, 1049, 1055, 1148], "field_disc": 328307557444402776721569, "field_disc_factorization": [[3, 10], [11, 18]], "field_poly": [1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "-0.005", "prec": 20}, {"__RealLiteral__": 0, "data": "19.334", "prec": 20}, {"__RealLiteral__": 0, "data": "167.768", "prec": 24}, {"__RealLiteral__": 0, "data": "5645.408", "prec": 27}, {"__RealLiteral__": 0, "data": "89418.351", "prec": 30}, {"__RealLiteral__": 0, "data": "2183687.174", "prec": 37}], "related_objects": [], "self_twist_discs": [-3], "cm_discs": [-3], "rm_discs": [], "relative_dim": 1, "trace_display": [0, 1, 0, -1], "traces": [0, 20, 0, 1, -2, 0, 0, -1, 0, 1, 0, 0, 1, -1, 0, 0, -2, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, -2, -1, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0, 21, 0, 0, 0, -9, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -20, -2, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 1, -1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, -9, 0, 0, 0, 0, -2, -1, 0, 2, -1, 0, 0, 0, 0, -9, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -9, 0, 0, -9, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -1, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 1, 2, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 2, 0, -2, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 2, 0, 1, -1, 0, 0, -10, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, -2, 0, 0, 0, -4, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 2, 0, 0, 0, -1, 0, -4, 0, 0, -1, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -9, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 12, 0, 0, 2, 0, 0, 0, 0, -1, 21, 0, 0, 0, 0, 0, -1, 0, -4, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 9, 1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, -12, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 20, 21, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, -2, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -13, 0, 0, 1, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 21, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, -12, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -12, 0, 0, 0, 0, 1, 2, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, -4, 2, 0, 0, -12, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 1, 0, 0, 2, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -9, 0, 1, 22, 0, 0, -2, 0, 0, 0, 0, -9, 0, 0, -4, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -4, -4, 0, 0, -1, 0, -2, 0, 0, -9, -1, 0, 0, 0, 0, 0, 2, 0, -13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, -12, 0, 0, -9, 0, 0, -1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, 0, 2, 0, 21, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, -9, -12, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, -9, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, -2, 0, -1, 0, 0, -1, 2, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, -4, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, -4, 0, -1, 0, 0, 0, -9, 0, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 1, 1, 0, 2, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, -10, 0, 1, 0, 0, 0, -12, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -9, 0, 0, -9, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -11, 2, 0, 0, 2, 0, 1, 0, 0, -2, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 21, -1, 0, -1, 0, 0, 0, 18, 0, 0, 0, 0, 0, -4, 0, 0, -1, 0, 0, 0, 0, -9, 0, 0, 0, 1, 0, -9, 0, 0, 0, 20, 0, 0, 0, 0, 0, -1, 0, 0, 20, 0, 0, 20, 0, 2, 0, 0, -9, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 21, 0, 0, -1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, -1, -1, 0, 0, -2, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, -4, 0, 2, -1, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, -1, 0, 0, -4, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 10, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, -12, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, -2, 0, 0, -9, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 4, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, -2, -1, 0, 0, 1, 0, 0, -12, 0, 2, 0, 0, 0, 0, 0, -1, 2, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, -4, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 22, 0, 0, -4, 2, 0, 0, 0, 0, 0, -1, 0, 9, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, -1, -12, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 2, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 20, -2, 0, 0, 20, 0, 0, 0, 0, -2, 2, 0, 0, 1, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 21, 2, 0, 0, 4, 0, 0, 0, 0, 0, 21, 0, 9, 0, 0, 0, -1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 2, 0, -10, 0, 0, 0, -10, 0, 0, -1, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 2, 0, 2, -1, 0, 0, 0, 0, -4, 0, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 21, 0, 0, -9, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, -9, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 1, 0, 2, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -13, 0, 0, 0, 0, 0, -11, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, -9, 0, -2, -2, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -10, 0, 2, 0, 0, 0, 1, 0, -4, -1, 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, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, -2, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 9, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, -1, 0], "projective_field": [14520518798861539888128, -18404471912796372407616, 9086688618789195133884, -3113604191168903779560, 1468196654209714473291, -594190140011390622231, 110665894154275707396, -17407952651281602948, 26287298965711108963, -19395063895919708649, 7671866082898474144, -2016467384844206002, 307283290099771750, 27670630004684528, -27716768908594182, 4604023919812490, 497960283475878, -214233452354616, 3014246804838, 3925917847200, 140466200016, -117051224280, 3743932008, 2466011778, -612473646, 15712320, 7037594, 701982, -128377, -257, 1118, -140, -3, 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, 3, 2, -1, 2, -3], [1, 1, 397, 11, 1, 33, 0], [1, 1, 1191, 28, -1, 66, 0]], "char_orbit_index": 28, "prim_orbit_index": 28, "minimal_twist": "1191.1.bb.a", "char_is_minimal": true, "conrey_index": 110, "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, 17]], [[1, 24]], [], [], [[-1, 32]], [], [[-1, 1]], [], [], [[1, 8]], [[1, 16], [-1, 21]], [], [], [[-1, 15]], [], [], [[1, 6], [-1, 19]], [], [[-1, 16]], [], [], [], [[1, 2]], [], [[1, 18]], [[1, 23]], [], [], [[1, 8], [-1, 13]], [], [], [], [], [[-1, 25]], [[1, 20], [-1, 23]], [], [[1, 0], [-1, 5]], [], [], [], [[-1, 11], [-1, 13]], [], [], [], [], [[1, 32]], [], [], [], [[-1, 7], [1, 12]], [], [], [], [], [[-1, 3], [-1, 23]], [], [], [], [[1, 14], [-1, 15]], [], [[-1, 0]], [[1, 6]], [], [], [[1, 14], [-1, 29]], [], [], [], [], [], [[1, 24], [1, 28]], [], [[-1, 19]], [[1, 10], [1, 30]], [], [], [[-1, 27], [1, 28]], [], [[1, 2]], [], [], [[1, 7]], [], [], [], [], [], [], [[1, 15], [-1, 20]], [], [[-1, 25], [1, 30]], [], [], [], [[-1, 3], [-1, 17]], [], [], [[1, 26]]]}