# Stored data for newform 1127.1.v.a, downloaded from the LMFDB on 25 April 2024.
{"label": "1127.1.v.a", "space_label": "1127.1.v", "level": 1127, "weight": 1, "hecke_orbit": 1, "hecke_orbit_code": 1443125789799, "dim": 20, "is_polredabs": true, "nf_label": "20.0.328307557444402776721569.1", "trace_hash": 1608151999305065039, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [], "qexp_display": "q+(-\\zeta_{66}^{23}-\\zeta_{66}^{29})q^{2}+(-\\zeta_{66}^{13}+\\cdots)q^{4}+\\cdots", "char_order": 66, "char_parity": -1, "char_degree": 20, "char_conductor": 161, "char_orbit_label": "v", "char_is_real": false, "Nk2": 1127, "analytic_conductor": 0.5624462692373937, "hecke_ring_index": 1, "level_radical": 161, "projective_image": "D11", "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": "0.506", "prec": 17}, "analytic_rank_proved": true, "char_values": [1127, 66, [346, 442], [11, 18]], "hecke_ring_generator_nbound": 4, "inner_twist_count": 8, "level_primes": [7, 23], "conrey_indexes": [31, 117, 215, 325, 374, 423, 472, 509, 558, 570, 607, 656, 717, 754, 864, 901, 913, 1048, 1060, 1097], "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": "-0.057", "prec": 20}, {"__RealLiteral__": 0, "data": "17.653", "prec": 20}, {"__RealLiteral__": 0, "data": "106.268", "prec": 24}, {"__RealLiteral__": 0, "data": "3551.641", "prec": 27}, {"__RealLiteral__": 0, "data": "46500.906", "prec": 30}, {"__RealLiteral__": 0, "data": "1054368.528", "prec": 37}], "related_objects": [], "self_twist_discs": [-7], "cm_discs": [-7], "rm_discs": [], "relative_dim": 1, "trace_display": [2, 0, 0, 0], "traces": [0, 20, 2, 0, 3, 0, 0, 0, -8, 1, 0, 2, 0, 0, 0, 0, -6, 0, 2, 0, 0, 0, -8, 1, 0, 1, 0, 0, 0, -4, 0, 0, -5, 0, 0, 0, 16, 2, 0, 0, 0, 0, 0, -4, -5, 0, 2, 0, 0, 0, 18, 0, 0, 2, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, -14, 0, 0, 2, 0, 0, 0, -4, 4, 0, -7, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 4, 0, -3, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, -4, 3, 0, 0, 0, 0, 0, -8, 2, 0, -9, 0, 0, 0, -4, 0, 0, 6, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -4, 8, 0, 0, 0, 0, 0, -8, 0, 0, 2, 0, 0, 0, 0, 4, 0, 5, 0, 0, 0, 10, 2, 0, 2, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, -4, -9, 0, 0, 0, 0, 0, -2, 0, 0, -5, 0, 0, 0, 2, 0, 0, -9, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, -9, 0, 2, 0, 0, 0, -4, -7, 0, 4, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, -4, -5, 0, 4, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 6, 2, 0, 0, 0, 0, 0, -4, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, -2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -8, 2, 0, 2, 0, 0, 0, -4, 0, 0, -5, 0, 0, 0, 10, 1, 0, 0, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 2, 0, 4, 0, 0, 0, 0, 3, 0, 4, 0, 0, 0, 0, -9, 0, 2, 0, 0, 0, 18, 2, 0, 0, 0, 0, 0, 28, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 14, -9, 0, 1, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 18, 0, 0, -7, 0, 0, 0, 14, 2, 0, 2, 0, 0, 0, 0, -7, 0, 6, 0, 0, 0, -10, -9, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -4, 4, 0, -3, 0, 0, 0, -12, 0, 0, 2, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 2, 0, 6, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, -1, 0, -7, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, -7, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -7, 0, -5, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -8, 0, 0, 1, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, -16, 0, -7, 0, 0, 0, -8, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -16, 2, 0, 2, 0, 0, 0, -2, -4, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 10, 0, 0, 2, 0, 0, 0, -4, 6, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -4, -3, 0, 4, 0, 0, 0, 6, 2, 0, 2, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 10, 2, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, -8, 2, 0, 0, 0, 0, 0, 18, 4, 0, 3, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, -4, 0, 0, 3, 0, 0, 0, 0, 2, 0, -9, 0, 0, 0, 0, 6, 0, 4, 0, 0, 0, -4, 0, 0, -9, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -12, 4, 0, 2, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -5, 0, -7, 0, 0, 0, -8, 0, 0, -18, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, -5, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, -4, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 4, 0, -5, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -8, 2, 0, 0, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, -4, 0, 0, -7, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 3, 0, 0, 0, 6, 0, 0, 2, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 4, 0, 1, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 2, 0, 0, 0, 0, 0, 18, -7, 0, -5, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, -4, 1, 0, 0, 0, 0, 0, 14, 0, 0, 2, 0, 0, 0, -4, -7, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, -5, 0, 0, 0, -16, -9, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, -4, -16, 0, 0, 0, 0, 0, 18, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, -7, 0, 2, 0, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, 2, 0, 3, 0, 0, 0, -4, 4, 0, -3, 0, 0, 0, -12, 0, 0, 2, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -8, 0, 0, 2, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 4, 0, 0, 0, -8, 2, 0, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, -4, 0, 0, -3, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -8, 4, 0, 2, 0, 0, 0, 0, -7, 0, -3, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 14, 0, 0, 2, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 14, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 10, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 12, 0, 4, 0, 0, 0, 36, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 12, 2, 0, 0, 0, 0, 0, -4, -3, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -12, 2, 0, 2, 0, 0, 0, 14, 6, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 6, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 14, 2, 0, 3, 0, 0, 0, -4, 0, 0, 12, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, 12, -9, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -8, -9, 0, 0, 0, 0, 0, -4, 0, 0, 8, 0, 0, 0, -12, 0, 0, -9, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -8, 2, 0, -9, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, -4, 0, -3, 0, 0, 0, -8, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 10, -9, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 4, 0, -5, 0, 0, 0, 0, 1, 0, -9, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, -4, 0, 0, -3, 0, 0, 0, -12, -9, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 2, 0, 0, 0, -4, -1, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, -12, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 14, 2, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 14, 0, 0, -7, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, -2, 6, 0, -5, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -4, 0, 0, -12, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 18, 6, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, -3, 0, 0, 0, 0, 0, 24, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -12, 2, 0, 2, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, -8, 0, 0, 6, 0, 0, 0, 14, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -8, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 10, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 4, 0, 6, 0, 0, 0, -6, 0, 0, 2, 0, 0, 0, -2, 8, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 4, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 4, 0, 6, 0, 0, 0, -16, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, -4, -7, 0, -7, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -8, -7, 0, -5, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, -7, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 2, 0, 2, 0], "projective_field": [-2025, 4891, 870, -2177, 181, 564, -330, 29, 21, 3, -5, 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, 7, 2, -1, 2, -7], [1, 1, 7, 3, 1, 3, 0], [1, 1, 7, 4, -1, 6, 0], [1, 1, 23, 3, 1, 11, 0], [1, 1, 161, 12, -1, 22, 0], [1, 1, 161, 13, 1, 33, 0], [1, 1, 161, 14, -1, 66, 0]], "char_orbit_index": 22, "prim_orbit_index": 14, "minimal_twist": "161.1.l.a", "char_is_minimal": false, "conrey_index": 31, "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, 23], [-1, 29]], [], [[-1, 13], [-1, 19], [-1, 25]], [], [], [], [[-1, 3], [-2, 9], [1, 9], [-2, 15], [1, 15], [-1, 21]], [[1, 20]], [], [[-1, 19], [1, 28]], [], [], [], [], [[-2, 5], [1, 5], [-2, 11], [1, 11], [-1, 17], [1, 26], [1, 32]], [], [[1, 10], [1, 16]], [], [], [], [[-1, 9], [-1, 15], [1, 18], [1, 24]], [[1, 2]], [], [[1, 4]], [], [], [], [[1, 18], [-1, 21]], [], [], [[-2, 1], [1, 1], [-2, 7], [1, 7], [-1, 13], [1, 16], [1, 22], [1, 28]], [], [], [], [[1, 0], [1, 6], [1, 12]], [[1, 14], [1, 26]], [], [], [], [], [], [[1, 12], [1, 30]], [[-1, 5], [1, 8], [-1, 11], [1, 14], [1, 20], [1, 32]], [], [[-1, 25], [-1, 31]], [], [], [], [[1, 0], [-1, 27]], [], [], [[-1, 1], [-1, 31]], [], [], [], [], [[1, 8], [-1, 11], [1, 14], [-1, 17]], [], [], [], [], [], [[-2, 3], [1, 3], [1, 6], [-1, 9], [2, 12], [-1, 12], [2, 18], [-1, 18], [1, 24], [1, 30]], [], [], [[-1, 1], [-1, 7]], [], [], [], [[-1, 3], [-1, 27]], [[1, 2], [1, 8], [-1, 23], [-1, 29]], [], [[1, 4], [1, 10], [1, 16], [1, 22]], [], [], [], [], [[1, 2], [1, 32]], [], [[-1, 7]], [], [], [], [], [[1, 2], [1, 8], [1, 20], [1, 26]], [], [[-1, 1], [1, 4], [-1, 7], [1, 10], [1, 16], [1, 22], [1, 28], [-1, 31]], [], [], [], [[-1, 15], [-1, 21], [-1, 27]], [], [], [], [], [], [], [[1, 6], [-1, 15]], [[-1, 17], [-1, 23], [-1, 29]]]}