# Stored data for newform 169.2.a.b, downloaded from the LMFDB on 07 May 2024.
{"label": "169.2.a.b", "space_label": "169.2.a", "level": 169, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660925097, "dim": 3, "is_polredabs": true, "nf_label": "3.3.49.1", "trace_hash": 591432028557783991, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [-1, -1, 2, 1]]], "qexp_display": "q+(-1-\\beta _{2})q^{2}+(-\\beta _{1}+\\beta _{2})q^{3}+(\\beta _{1}+\\cdots)q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 676, "fricke_eigenval": 1, "atkin_lehner_string": "+", "analytic_conductor": 1.3494717941596386, "hecke_ring_index": 1, "level_radical": 13, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 14, "field_poly_is_real_cyclotomic": true, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.006", "prec": 17}, "analytic_rank_proved": true, "char_values": [169, 1, [2], [1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [13], "conrey_indexes": [1], "field_disc": 49, "field_disc_factorization": [[7, 2]], "field_poly": [1, -2, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.906", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "21.311", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "224.603", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[13, 1]], "trace_display": [-2, -2, -4, -3], "traces": [0, 3, -2, -2, 0, -4, -1, -3, -3, -3, 5, -8, 0, 0, -5, -2, 2, -2, 9, -4, 0, 2, 3, -5, 9, -5, 0, 1, 14, -1, -1, -5, 7, 10, 13, 4, -7, 12, 12, 0, -3, -7, 8, 13, 0, 11, 8, -18, 1, -4, 1, -1, 0, 1, -3, 6, -4, 5, 3, -19, 7, 4, 1, -4, -11, 0, 5, -1, -21, -6, 2, -27, -4, 9, -8, 15, -21, 8, 0, -5, -5, -1, -14, -7, -7, 5, -18, -18, 15, -11, -12, 0, 0, 22, 5, 3, -21, 7, 5, 1, -7, 5, -11, -3, 0, 9, -24, 2, 14, 20, -11, -15, -9, 27, -8, 16, 14, 0, 22, -19, -5, -7, -12, 28, -14, 15, 5, -22, 19, 3, 0, -17, -7, -17, 10, 8, 9, 20, -3, -14, -21, 12, 11, 0, -2, 20, 22, 5, 7, 12, 4, -1, 18, 16, 18, -12, 0, -9, 43, 25, 7, 5, -25, 40, 14, 3, -7, -14, -16, 0, -15, 11, 7, -24, -2, -2, -3, 22, -9, 15, 0, 28, 0, -19, -9, -9, 4, 3, 14, 13, -16, -5, -2, 6, -35, 0, -7, 1, -24, -16, 26, -25, -43, 15, 14, -14, -12, 19, 0, 13, -6, 6, 21, 11, 15, -29, -22, -9, 10, 1, 7, 0, -4, -21, 14, -9, -11, -5, 7, -39, -13, -17, -34, -19, 0, 24, -28, -13, 22, -48, -6, -12, 21, 21, 35, 3, 21, 0, 40, -21, -31, 0, -21, 4, 31, -8, -28, 25, 5, -5, 0, 22, -5, 8, -31, -27, 30, -9, 7, -16, 4, -25, 8, 0, -4, 25, 14, 15, 7, -16, 24, -13, 13, -2, 21, -9, 0, 21, 7, -17, -4, 14, -63, -28, -1, 16, -26, -12, -15, 0, -14, -6, -18, 27, 9, 11, -27, 14, -35, -19, -6, -9, 0, -38, 27, -11, -63, 40, 23, -16, 24, 1, -1, 33, 28, 0, -15, -32, 35, 32, 5, 5, 49, -5, 70, 27, -1, -29, 0, -25, 28, 32, -33, 18, 1, 8, 16, -27, 21, -28, 27, 0, -35, 9, -3, 43, 49, 15, -3, -23, 3, -19, 21, -21, 0, -19, 8, 26, -8, -35, 20, 20, -21, 9, -37, 4, 11, 0, -25, 50, 35, 38, -48, -18, 20, 1, -32, -34, 42, 22, 0, 8, 11, 2, 18, 23, 28, 3, 48, 2, 6, 40, -9, 0, 49, -22, -31, -39, 8, -12, 7, -4, 49, -9, -15, 35, 0, 49, -32, -77, -7, -55, 31, 11, 27, 8, 16, 31, -35, 0, 31, -29, -11, -14, 41, 17, -28, 2, -31, 4, 1, 4, 0, 44, 7, 31, 21, -15, -31, -13, -22, 42, -7, -32, 8, 0, -5, -23, 12, -17, -14, -35, -26, -6, -17, -13, 15, -38, 0, 8, -23, -8, 47, -23, -38, 23, -21, -50, 11, -82, 14, 0, -41, 20, -7, -28, 35, 27, -46, -29, -9, 55, -42, -11, 0, -20, 13, 48, 14, 33, 28, -28, -70, 0, 39, -37, -19, 0, -56, -11, 10, -72, -24, -27, 37, 25, -21, 48, -34, 72, 0, -65, 11, -59, 42, -29, -52, 15, 2, -42, 25, 19, -28, 0, 20, -5, -41, -31, -1, 13, -35, 75, 26, -35, -28, -8, 0, 34, -28, 3, 2, -29, -1, -58, -10, -1, -35, 34, -29, 0, 19, 12, 25, -44, -7, -29, 20, 29, 6, -47, 13, -27, 0, 15, 21, -15, 46, 86, -26, 38, -49, 56, 28, 23, 33, 0, 77, 42, 0, 37, -41, 18, 1, -18, 8, 23, 21, -29, 0, 8, -29, 21, -17, 36, 70, 35, 38, -31, -49, 39, 16, 0, 42, -43, 42, 0, -8, 43, 15, 9, 49, 17, 55, 60, 0, -9, 2, -11, -28, -15, -9, 57, 12, -4, -92, 6, -49, 0, -8, 27, -58, 92, -17, 49, -28, -11, -71, -16, 22, 60, 0, -43, -21, 44, -30, 32, 0, 12, 16, 69, -14, -12, 48, 0, -56, 32, 43, 39, -84, 0, -11, -27, 35, 34, -25, -32, 0, -80, -16, 35, -26, 29, 2, 6, 56, -36, 51, 61, 11, 0, -3, 66, -56, 27, 46, -21, 18, -28, 14, 1, -21, -57, 0, -30, 20, 19, -41, 44, 0, -30, -38, 61, -38, -29, -3, 0, 7, 53, 76, 4, 12, 52, -41, 36, -63, -52, -14, -7, 0, -18, -13, -25, 7, -11, -71, -2, 21, -23, -7, 48, -21, 0, 3, -69, -36, -9, 8, 21, 56, -37, 16, 44, -19, 42, 0, 34, 7, -43, -59, 16, -31, -18, -9, -48, 91, -12, -44, 0, 35, -35, -10, 2, 14, -89, 46, 62, 0, 22, -94, 0, 0, 65, -17, 51, 2, 26, 22, -26, -56, 39, -48, -34, 13, 0, 19, -3, -35, -21, -13, -9, -63, 11, 13, -17, 35, -30, 0, 6, 16, -62, 24, -49, -7, -37, 12, -51, -3, -22, 71, 0, 14, 12, -16, -27, -53, -54, 69, 43, -7, 68, 0, -45, 0, 12, 7, 56, 49, -53, 63, -42, 5, 2, 74, -17, -70, 0, -40, 0, 3, -78, -45, -6, 0, -112, -58, -10, 19, 75, 0, -10, 7, -70, 80, -51, 56, -24, -35, 9, -21, -3, -16, 0, -34, -56, -20, 13, 21, 19, -47, -35, 4, -77, -19, 55, 0, -6, -34, 32, 43, -34, -2, 26, 0, 3, 3, 1, 23, 0, 46, -87, 49, -45, 49, -24, -34, -21, 19, -13, -35, -75, 0, 69, 1, -7, 13, 23, -7, 59, 44, 51, 19, -28, 70, 0, 35, -41, -38, 10, 84, 52, 18, 17, 7, 34, 121, -18, 0, 63, -31, 51, -21, 9, -18, -35, 6, -43, 41, -9, 56, 0, -41, 34, 33, 27, 24, -5, 21, 55, 71, -48, -9, 4, 0, 12, 70, -50, -4, -20, -28, -15, 42, -17, -91, -21, -137, 0, -23, 76, -25, 13, 14, 22, -25, -68, -63, -20, 40, -19, 0, -45, 25, -41, -98, -29, 17, 61, 14, 33, -29, 25, -8], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "169.2.a.b", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0], [1, 0, 0], [-1, 0, -1], [0, -1, 1], [0, 1, 1], [-2, 1, -1], [0, 0, 1], [-1, 1, 1], [0, -2, 1], [-2, 1, -2], [2, 0, 1], [-2, -1, 1], [-1, 1, -2], [0, 0, 0], [-1, -2, 0], [-1, 1, 0], [1, -1, 0], [-1, -1, -2], [3, 1, 1], [-1, -2, -1], [1, -3, 0], [-1, 2, -3], [2, 0, 3], [-3, 2, -2], [2, 1, -2], [0, -3, 2], [0, 0, 0], [-1, 3, -1], [5, 0, 1], [-3, 5, -3], [0, -1, 0], [1, -5, 3], [0, 5, -2], [1, 3, -4], [4, 3, 2], [3, -4, 1], [-1, -4, 0], [3, 2, -1], [4, 3, 3], [0, 0, 0], [-2, 3, 0], [1, -4, 6], [2, 1, -1], [6, -2, 3], [-1, -1, -4], [5, -2, 2], [3, 0, 1], [-6, 1, 1], [1, -1, 1], [-1, -1, 0], [1, 1, 3], [1, -1, 3], [0, 0, 0], [4, -4, 7], [-1, -2, -2], [3, -1, 2], [-4, 3, -5], [2, 0, 1], [1, -2, -2], [-5, -4, 0], [3, -1, 1], [-1, 6, -1], [1, 2, 4], [1, -5, 2], [-5, -1, -5], [0, 0, 0], [0, 1, -4], [-4, 6, -5], [-7, -3, -3], [-2, 1, 1], [0, 3, 1], [-10, 3, 0], [-1, 2, 3], [4, -6, -3], [-4, -1, -5], [3, 2, -4], [-8, -2, -5], [1, 0, -5], [0, 0, 0], [-4, -1, -8], [-3, 3, -1], [3, -3, 7], [-3, -2, 3], [-6, 9, -2], [0, -4, 3], [1, 3, 1], [-7, -1, -4], [-5, 0, 3], [2, 5, -4], [-6, 7, 0], [-5, 0, -3], [0, 0, 0], [2, -5, 1], [5, 2, -5], [4, -2, 5], [0, 4, 1], [-5, -2, 4], [5, -1, 7], [2, 1, 2], [3, -2, 6], [-5, 2, -6]]}