# Stored data for newform 187.2.a.e, downloaded from the LMFDB on 25 April 2024.
{"label": "187.2.a.e", "space_label": "187.2.a", "level": 187, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014398543036603, "dim": 3, "is_polredabs": true, "nf_label": "3.3.148.1", "trace_hash": 993303310140749651, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [-2, -2, 2, 1]], [3, [-5, -1, 3, 1]]], "qexp_display": "q+(-1+\\beta _{1})q^{2}+(-1-\\beta _{2})q^{3}+(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": 748, "fricke_eigenval": 1, "atkin_lehner_string": "++", "analytic_conductor": 1.493202517797943, "hecke_ring_index": 1, "level_radical": 187, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "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": "0.009", "prec": 17}, "analytic_rank_proved": true, "char_values": [187, 1, [35, 122], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [11, 17], "conrey_indexes": [1], "field_disc": 148, "field_disc_factorization": [[2, 2], [37, 1]], "field_poly": [1, -3, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.854", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "22.418", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "267.260", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[11, 1], [17, 1]], "trace_display": [-2, -3, -7, 0], "traces": [0, 3, -2, -3, 2, -7, 4, 0, -6, 2, -2, -3, -12, 0, -4, 5, 4, -3, -10, 6, 4, -16, 2, -15, 22, 8, 20, -3, 20, -14, 6, -9, -4, 3, 2, 4, 20, -11, -20, 6, 10, 0, 24, 8, -2, 4, 12, 16, -8, 11, 26, 3, -26, -30, 18, 7, -32, 4, -2, -1, 6, -6, 22, 20, 4, -20, -4, -13, -2, 23, -8, -3, -24, -12, 4, -6, 10, 0, -46, 14, 4, -13, -4, 8, -28, 7, -24, 18, 6, 1, 6, -12, -20, -1, -10, 2, -8, -17, -26, -2, -28, 0, -4, -4, 12, 24, 38, -16, -8, -22, 2, 47, 8, 13, 30, 33, -2, -26, 36, 0, -34, 3, 8, -16, -12, -15, -40, 14, 32, 16, -34, 10, 12, -20, 14, -9, 6, -25, -32, 14, -20, -38, 22, 0, 20, 44, 10, 13, -40, -24, -54, 30, 8, -2, 4, 5, 66, 3, 6, 28, 0, -16, 4, 12, 20, -5, -32, 0, 40, 21, 2, 10, 0, -4, 0, -4, -4, 19, -22, 31, -16, -3, 52, 22, 46, 29, -34, 3, 32, 20, 38, 11, 4, 22, -4, 28, 2, -46, 10, 8, -12, -15, -24, -8, 12, 4, -54, -20, -40, -6, -12, -22, -36, 9, 18, 0, -14, 20, 62, 20, -4, 0, -44, -51, 24, -28, -42, -26, -62, 1, 14, 16, 36, 26, 52, -38, -54, -2, 4, -4, -12, -8, -2, 28, -24, -7, 24, -48, -2, -16, -56, 55, 48, 15, -28, -5, -56, 2, 24, -72, 26, -2, 36, -24, -22, 52, -20, -37, 14, 54, -40, -18, -4, 40, 22, -8, 74, -10, -34, -12, 48, 8, 42, -38, -28, -42, -20, 32, 0, 3, 36, 5, -18, -28, 28, -33, 94, 3, -8, 6, 64, -48, -36, -22, 40, 10, 10, 46, -20, -50, -36, -12, -52, -9, 10, -20, -18, -55, -74, 14, -36, -4, 40, -6, -10, 94, 36, 14, -32, 44, -6, -27, 40, -40, 30, 25, -48, 8, -12, -23, -4, 9, -32, -48, 32, -37, 0, 14, 26, -32, 56, 48, 4, 9, -90, -13, 58, 16, -22, 2, 12, 23, 0, -3, -80, 26, -32, 3, -24, 20, 50, 4, 74, 30, -2, 47, -76, -34, 16, 15, 2, 10, -26, -15, -40, -4, 10, 0, 16, -1, 60, 15, 26, 62, -2, -48, -20, 4, 60, -64, -52, -24, 0, 48, 46, 35, 4, 11, -22, 10, -8, -3, 108, -36, 70, 8, 28, -14, 20, 72, -4, 6, 68, 32, 56, -8, -50, -32, 2, -6, 56, -38, -36, -9, 24, -54, -54, -20, -28, 32, -10, 2, -20, 3, 70, 19, 12, 2, -16, -55, 40, 0, 52, -20, -42, -16, 56, -16, -72, 3, -10, 52, -24, 15, 4, 37, -48, -25, -92, 56, -34, 45, 38, -8, -24, -74, -20, -36, 8, 4, 36, -10, 68, 84, 2, 55, -68, -63, 44, 16, 54, -18, -28, 14, 26, -4, -44, -12, 72, 18, 24, -28, -6, 24, -56, 24, -12, -87, 4, -27, -6, -16, 8, -74, 66, 66, -64, -16, 80, -56, 56, -23, 32, -8, -108, 20, 12, 9, 8, 14, -18, -54, 104, -12, 80, 30, -30, 13, -40, -11, 2, 18, -16, -5, 4, 4, -132, 48, 6, -24, -26, 14, -130, -24, -76, -97, 34, -108, 42, -56, 16, -3, -4, 12, -84, 3, 2, -12, 18, -36, -36, 6, 26, 13, -40, -38, -32, 23, -2, -22, -26, 16, 20, 30, 40, 26, 36, -4, -76, -86, -52, 14, -8, -78, -18, -4, 30, 56, -126, -12, -8, 38, 0, 14, 26, -7, 70, 14, -60, 52, 12, 2, -20, 2, -32, 24, 32, 10, 162, -17, -6, 5, -20, 72, 92, 61, 2, -4, -58, 11, 32, 13, -4, 38, 34, -14, 172, -56, 2, -28, -48, 49, -16, 23, -108, -72, 20, -37, 38, 1, 16, 80, -64, -77, -116, -66, 8, -18, -64, 42, -6, 75, -38, -6, -32, 80, 102, 74, -2, 37, -30, 6, 40, 38, -4, 82, 78, 52, 94, 24, -10, -14, -22, -60, 84, 53, 24, -15, 48, 54, -24, 1, 60, -20, -56, -8, -88, 0, -20, -50, -72, 28, -6, 60, -4, 72, -52, 44, 128, -19, -32, -18, -74, 35, -24, 20, -22, 50, 8, -63, -12, 108, -8, 12, 8, -98, 4, -43, 80, 11, 12, -8, 52, -26, -38, -67, 8, 13, -40, -8, 18, 98, 72, 56, -78, 80, -84, 40, 2, 40, 80, -51, 20, -31, -94, -54, -84, -50, -10, -23, -84, 10, 32, 16, 2, -4, 78, 106, 96, -22, 8, -4, -10, 26, -16, 66, 10, 52, -44, -20, -54, 3, -12, -28, 52, -19, -144, 16, 34, 82, -28, 20, 24, 12, -54, -10, -124, -1, 124, -16, 48, 58, 82, 12, 40, 8, -46, -70, -44, -24, 24, 42, -48, 54, -4, -72, 8, 120, -72, -80, -20, 16, -16, -17, -100, 6, 108, 24, -124, -29, 40, -74, 80, -11, 68, -30, -10, 77, -8, -7, -16, 5, -102, 22, -84, -51, -96, 0, -76, -6, -26, 91, 78, 0, 48, 2, -8, 30, 46, -85, 16, -8, -2, -64, 56, 12, 88, -3, -124, -14, -62, 16, 28, 16, 110, -64, 62, -90, 86, 48, -4, -15, -26, 24, 26, 33, -16, -40, -146, -48, 6, 13, 2, -14, 38, -71, 16, -50, 84, 0, -76, 30, 4, -80, -46, 9, 62, -80, 82, 46, -52, -66, -60, -8, 60, -34, 86, -144, -18, -48, -74, -76, 0, 60, 28, -82, 24, 108, -12, 26, 30, 126, 72, 48, -20, -7, 132, -20, -28, 67, 0, 10, -68, -16, -72, -76, 24, -43, 2, 6, -20, 69, 32, 26, 132, -7, -54, -18, -84, 56, 44, 2, -178, 2, -72, -76, -148, 80, -6, -4, 30, 41, 68, 0, -40, -174, -16, -57, -100, -1, 20, -54, 140, -21, 40, 140, 2, -84, -76, -16, -6, -32, 64, -49, 56, -84, -120, 46, -46, -71, 94], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "187.2.a.e", "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, 1, 0], [-1, 0, -1], [1, -1, 1], [-2, -1, 0], [2, -2, 1], [0, 0, 2], [-2, 0, -2], [1, -1, 1], [0, -2, -1], [-1, 0, 0], [-5, 3, -1], [-1, 3, 0], [-2, 2, -2], [1, 2, 2], [2, -2, 0], [-1, 0, 0], [-4, 2, -2], [3, -3, -2], [1, 1, -1], [-6, 2, 0], [1, -1, 0], [-5, 0, -1], [8, -2, 2], [1, 5, 1], [7, -1, 3], [-2, 3, 2], [8, -4, 0], [-4, -2, -1], [1, 3, 0], [-4, 3, 2], [-2, 2, 2], [1, 0, 1], [1, -1, 0], [2, -2, -4], [8, -4, 2], [-3, -2, -5], [-7, 1, -1], [4, -6, 1], [2, 4, 4], [0, 0, 2], [10, -6, 2], [4, -4, -4], [-1, 1, -1], [1, 1, -1], [6, -6, 1], [5, 1, 3], [-4, 4, -2], [5, -4, -4], [8, 2, 4], [1, 0, 1], [-10, 4, -4], [-11, 3, 1], [6, 0, 1], [2, 1, 0], [-12, 4, 0], [0, 4, -3], [1, -5, -1], [-2, 5, -1], [3, -3, -1], [-2, 0, -2], [8, -2, 1], [8, -4, 0], [0, 4, 0], [-4, -8, -3], [-2, 2, -1], [-5, 2, 4], [-1, 1, -1], [8, -1, 5], [-2, -2, 2], [-2, 3, 0], [-10, 6, -2], [-4, 0, -1], [4, -8, 3], [1, -9, -1], [4, -2, 6], [0, 0, -2], [-17, 5, -7], [4, 2, -1], [0, 4, 2], [-4, -1, -1], [-2, 2, -2], [4, -4, 0], [-12, 8, -8], [2, 1, 0], [-8, 0, 0], [5, 3, 4], [2, 0, 2], [1, -2, 4], [2, 0, 2], [-6, 6, -2], [-9, 7, -5], [1, -4, 4], [-6, 8, -2], [-2, 8, 7], [-2, -2, 2], [-5, -2, 1], [-9, 1, 0], [-1, 1, -1], [-10, 2, -4]]}