# Stored data for newform 117.2.e.a, downloaded from the LMFDB on 19 April 2024. {"label": "117.2.e.a", "space_label": "117.2.e", "level": 117, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 274911461493, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 890005610805248567, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [4, 2, 1]]], "qexp_display": "q+(-2+2\\zeta_{6})q^{2}+(-2+\\zeta_{6})q^{3}-2\\zeta_{6}q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "e", "char_is_real": false, "Nk2": 468, "analytic_conductor": 0.9342497036489805, "hecke_ring_index": 1, "level_radical": 39, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.011", "prec": 17}, "analytic_rank_proved": true, "char_values": [117, 3, [92, 28], [1, 3]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [3, 13], "conrey_indexes": [40, 79], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.970", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.900", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "106.747", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [-2, -3, -4, -2], "traces": [0, 2, -2, -3, -2, -4, 0, -2, 0, 3, 16, -2, 6, -1, -4, 12, 4, -10, 6, -12, -8, 0, -4, 3, 0, -11, 4, 0, 8, 2, -24, -4, 8, 0, 10, 16, -12, -4, 12, 3, 0, 6, 12, 3, 8, -24, -12, -6, 0, 3, -22, 15, -2, 6, -18, 16, 0, 18, 4, -12, 0, 5, 16, 6, -16, -4, 12, -4, 10, -9, -16, 24, 0, -8, 4, 0, 12, -4, -6, -5, -32, -9, -24, -2, -12, 20, 6, 0, 0, -20, 24, 4, 6, 12, -12, 24, -24, 8, -12, 6, 44, -9, 0, 0, 0, -24, -6, 6, 18, -28, -16, 6, 8, -21, 0, 12, -8, -6, 48, 10, 0, 7, 10, -18, -8, 48, -24, -32, 0, 0, -8, 1, -12, 12, 16, 36, 0, 12, 18, 3, -16, 0, -24, 4, -12, -16, 8, -9, 4, 0, 66, 2, 0, -15, 16, -16, 0, -21, -10, -9, 32, -12, 36, -32, 12, -24, -4, -2, 0, -1, -80, -18, -12, 3, -12, -22, 8, 36, 20, -38, 24, 22, -4, 0, 0, 8, -24, 10, 24, -18, -96, -19, 24, 24, 16, 0, 6, 48, -24, 34, 0, 12, -18, 4, -30, 24, 0, 18, -8, 12, 0, -1, -6, -36, -6, -24, 0, 16, 28, 12, -16, 5, 0, -16, -32, 33, 84, 4, -36, 16, 24, 12, 0, -14, 6, 48, -24, 0, 20, 6, 48, -4, -28, 27, -20, 12, 36, 6, 0, 0, -48, -30, 12, -12, 32, -60, -16, -13, -18, 4, 16, -6, -4, -15, 0, -12, 24, 30, -8, -20, 0, 48, -20, -6, 24, -22, 0, -14, -12, -24, 0, -4, 36, 15, -24, -72, -4, -24, 48, 16, 16, 0, 8, 18, 18, -48, 0, -18, 0, 3, -66, 6, 4, 0, -24, -40, -30, -32, -8, 0, -32, 0, 0, -6, 84, 24, 20, 8, 0, 4, 32, -9, 12, 60, -18, 22, 32, 42, 0, -12, 0, 4, 8, -6, 8, -16, -24, -27, -2, 63, 40, 16, -36, -40, 0, 0, 6, -33, 12, 8, 88, 9, -32, 10, -72, -48, 20, 0, 38, 0, 0, 34, -22, -21, -4, 16, -30, 5, 24, 36, -32, -6, 0, -1, 20, -72, 0, -4, 36, 12, 48, 48, -38, -34, 0, -16, -96, -9, -32, 1, 24, -15, 0, -3, -48, 40, 12, 16, -34, 0, 44, -26, -24, -4, 36, -36, -16, 4, 0, 32, 48, 0, 0, 48, -18, 16, 8, -9, 24, 1, 48, -26, 4, 18, 0, 55, 0, 10, -6, -6, 24, 0, 36, -70, -16, 24, 28, -18, 0, 1, 0, 18, -20, -31, -12, 40, -32, 0, 16, -8, -132, -24, -42, 0, 8, -8, 0, 16, -64, 0, -48, 22, -24, -16, -8, 0, 14, 6, 6, 16, -48, 63, 0, 6, 30, 66, -40, 9, -24, -36, 0, 2, -8, 18, 14, -64, -54, 36, 0, 48, 24, -12, 0, -10, -24, 24, -32, -24, 12, 0, -48, 6, 30, 58, 0, 72, 12, 0, 32, 16, 120, 8, 64, 0, 52, 0, 18, -12, 8, 0, 0, 36, 24, -56, 2, 66, -30, 20, -24, 14, 48, -72, -48, 6, 0, -12, 0, 57, 20, -12, -72, 72, -48, -33, -40, 56, 0, -28, -48, -15, 88, -12, 0, -10, -28, -24, 6, -36, 24, -6, 32, 0, -8, 21, -36, -84, -60, 36, 0, -38, 144, -20, -4, 0, 24, -66, -24, 64, -16, -72, 16, -4, -48, -6, 0, 12, -72, 22, 0, 24, -96, -72, -8, -44, 36, -80, 0, -51, 6, -31, 0, 35, -24, -24, -8, 28, 54, 1, -48, -12, 40, 12, 60, 20, 32, 0, 0, 40, 0, 24, 64, -27, 0, 20, 12, -41, -12, 0, -42, 20, 48, -68, 0, 3, 16, 64, 18, 3, -16, 36, 0, 14, 0, 34, 12, 36, -60, -2, 0, 48, -22, -24, 32, 18, 0, 4, 48, -12, 48, 40, 48, -48, 8, -15, 0, -96, -12, 12, -4, 0, -32, 10, 48, 41, 108, -99, 4, -38, -126, 16, 0, 0, -16, 84, 72, -96, 40, -48, -12, -3, -72, -42, -12, -24, 132, 12, 0, -30, 16, 21, -44, -10, 0, 24, 16, -72, 20, -18, 0, -34, 192, 15, 0, 12, -60, -8, 38, -18, 0, 48, -48, 0, -34, 0, -22, 22, 42, 13, 0, -54, -64, -15, 30, -6, 10, 0, -24, 16, -36, -44, 16, -18, -12, -18, 0, 0, 4, 6, -40, -6, 0, 28, 24, 45, 4, -16, 0, -34, -12, 18, 0, 2, 0, 28, 76, 120, 136, -12, 48, -24, -32, 39, 48, -8, 36, 88, 0, 0, 2, -36, -24, -24, 60, 18, 24, -84, 6, 20, -48, 0, -40, 84, 0, -10, -16, 36, -34, -2, -72, 30, -176, -30, 104, 8, 0, 24, -8, 30, 0, -6, -72, -104, 8, -72, 8, 64, 0, -18, -128, 6, -96, 8, -72, -27, 0, 66, -48, 4, -18, -92, -16, 0, 8, -15, 18, -8, -48, 36, -4, 36, 0, 25, -52, 0, -2, 8, -72, -28, 12, -45, 110, -6, 72, -36, -40, 144, 0, 14, 0, 41, 24, 36, 0, 88, -72, -24, 70, -24, -16, -10, 0, -4, 0, -24, 72, -48, -24, -2, 2, -54, 32, -14, -18, -40, 10, 0, -62, 15, 0, 32, -160, 36, 64, 36, 0, 76, 0, 0, 8, -16, 66, -30, 24, -18, 0, -44, -12, -33, -16, 27, 32, 17, 0, -4, 32, 60, 32, -4, 90, 30, 0, 48, 44, -12, 0, 22, 64, 0, 32, -6, 96, -18, 14, 0, -6, -80, 0, 46, -16, 0, -48, 10, -126, -18, -96, 0, -24, -18, -30, 4, 132, 0, 0, 36, 18, 152, 12, -12, -72, 24, -96, 15, -8, 9, 16, 96, 0, -32, 0, -90, 64, -72, 0, -12, -36, -33, -20, 36, 0, 20, -48, -42, 48, 52, 0, -96, -20, 36, 12, 18, 48, 74, 32, 0, -48, -68, -12, 17, 0, 0, 0], "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, 9, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "117.2.e.a", "char_is_minimal": true, "conrey_index": 40, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [-2, 2], [-2, 1], [0, -2], [0, -4], [2, -4], [-2, 2], [0, 0], [3, -3], [8, 0], [-2, 2], [2, 2], [0, -1], [0, -4], [4, 4], [4, -4], [-5, 0], [0, 6], [-6, 0], [-8, 8], [2, -4], [0, -4], [0, 3], [0, 0], [-11, 11], [2, 0], [-3, 6], [4, 0], [2, -2], [-16, 8], [0, -4], [0, 8], [2, -4], [10, -10], [8, 0], [-6, 0], [-2, 0], [12, -12], [1, 1], [0, 0], [0, 6], [4, 4], [3, -3], [4, 0], [-12, 0], [-6, 0], [-6, 6], [-4, 8], [0, 3], [0, -22], [10, -5], [-2, 2], [3, 0], [-6, -6], [8, 0], [0, 0], [12, -6], [0, 4], [0, -12], [8, -16], [5, -5], [8, 0], [0, 6], [-8, 0], [-4, 4], [4, 4], [0, -4], [0, 10], [-3, -3], [-16, 16], [12, 0], [0, 0], [-4, 0], [4, -4], [11, -22], [0, 12], [0, -4], [-4, 2], [-5, 5], [-16, 0], [0, -9], [-12, 0], [-2, 2], [-8, 4], [0, 20], [0, 6], [-2, 4], [0, 0], [-10, 0], [24, -24], [2, 0], [6, -6], [4, 4], [0, -12], [0, 24], [-8, -8], [8, -8], [-6, 0], [0, 6], [22, 0]]}