# Stored data for newform 187.2.g.e, downloaded from the LMFDB on 19 April 2024. {"label": "187.2.g.e", "space_label": "187.2.g", "level": 187, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014810859897019, "dim": 8, "is_polredabs": true, "nf_label": "8.0.13140625.1", "trace_hash": 1379987764567199672, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [1, 1, 10, -11, 9, -1, 0, 1, 1]], [3, [1, 3, 5, 3, 4, -3, 5, -3, 1]]], "qexp_display": "q+(-\\beta _{1}+\\beta _{5})q^{2}+(-\\beta _{2}+\\beta _{3}-\\beta _{4}+\\cdots)q^{3}+\\cdots", "char_order": 5, "char_parity": 1, "char_degree": 4, "char_conductor": 11, "char_orbit_label": "g", "char_is_real": false, "Nk2": 748, "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": false, "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": [187, 5, [35, 122], [4, 5]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [11, 17], "conrey_indexes": [69, 86, 103, 137], "field_disc": 13140625, "field_disc_factorization": [[5, 6], [29, 2]], "field_poly": [1, 3, 5, 3, 4, -3, 5, -3, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.018", "prec": 17}, {"__RealLiteral__": 0, "data": "7.650", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "182.974", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "8021.564", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c5", "trace_display": [-1, 3, -3, 3], "traces": [0, 8, -1, 3, 5, -3, 6, 3, 6, 5, 12, 2, 2, 3, 0, -10, 7, 2, 4, -5, -4, 6, -9, -24, -7, -3, -19, 3, 16, 10, -1, 17, -24, -8, -4, 6, -1, -13, -38, -11, 15, -22, -9, 8, -5, -24, -20, 9, 13, 1, -1, -3, -18, -23, 22, -12, 2, 16, -6, -35, -1, -19, -6, -4, 8, 10, 24, -10, 5, 12, 3, -5, 19, 39, -7, 6, 32, -3, 6, -3, 21, 7, -5, 29, 8, -2, -14, 32, 9, 40, 9, 21, 12, -14, 40, 23, -12, -5, 30, 20, -12, -20, 4, 14, -12, -9, 31, -7, -27, 38, 3, -12, -5, 13, -5, -8, -6, 27, -28, -3, 4, 38, 52, 1, -17, -5, -23, 24, -37, 9, 34, -28, -37, -52, -5, 24, -6, 18, -28, -54, -5, -47, 12, 2, 42, -4, 14, -28, 32, 6, 9, -1, 12, 10, -50, -50, -21, -21, 36, -13, 25, -16, -11, -15, -34, 10, -94, -59, -5, 25, 3, 22, 7, -20, 30, 24, 28, -14, -51, -10, -19, -29, -69, -17, -56, 6, 34, 8, -72, 25, 12, -24, -24, -35, 20, 22, -13, 2, -4, 72, 37, -15, -16, 16, -7, 21, 14, -8, -42, 30, 12, -4, 0, -49, -59, -20, -26, 9, 40, 50, -36, 2, -11, 15, 17, -17, 14, -22, -33, 46, -24, 14, 44, 5, 40, 48, 12, -3, 0, 21, 7, -20, 19, 42, -41, -18, -4, 96, 42, 21, 16, -14, 44, -56, 74, -5, -13, 65, 21, -45, 9, 4, 13, -24, 12, -42, 81, 22, -5, 37, -25, 7, 3, 15, -36, -42, 56, 7, -31, -2, 22, -4, -2, 45, 2, 22, 19, -18, -41, -2, 4, 45, 7, 16, 12, 33, 16, 12, 32, 32, 1, -29, 4, -18, -24, -15, -4, 18, 64, 0, 51, -22, 12, 51, 39, -15, 65, -24, -46, -10, 26, 49, -24, 5, -12, 1, 13, 61, 32, 86, -14, -156, 69, -13, 27, 10, 13, -61, 24, 13, -16, 53, -94, 3, -17, -28, -13, 4, 14, 86, -31, -128, -56, 42, -45, -27, 59, 4, 49, -60, -22, -91, -54, 38, 98, -1, -13, -28, -20, -14, -20, -58, -34, -176, -1, -42, -19, -18, -31, -52, -37, -75, -30, -34, -20, 29, 54, 37, -25, -12, -15, -16, -6, -87, 49, -72, -39, 44, -55, -1, -3, 73, -15, 61, 24, 15, -68, 13, 2, 28, -22, 48, -3, -47, -36, 32, -37, -46, -152, -32, -11, -103, 100, 18, -11, 3, 30, 47, 52, -44, 4, 8, -29, 32, -116, -6, 51, -4, 13, 8, -15, -8, -31, 19, -40, -34, 56, -92, 52, -60, 30, 42, 80, 30, 26, 46, 49, 72, -44, 2, 20, 40, -6, -120, 32, 3, 35, 19, -61, 10, 14, 20, -188, 77, -6, -11, 9, -75, 36, -34, 29, 78, -24, 16, -45, 60, 83, 39, 41, 19, -24, -33, -47, 20, -120, 19, 72, 33, 33, -12, 41, -27, 48, 69, -34, 36, 20, 2, 2, 32, 1, 32, -96, 14, 93, -1, -16, 1, 126, -34, 9, -28, 12, 2, -53, -10, 132, 28, -13, 104, -37, 82, -48, 16, 15, 10, 10, -18, 52, 4, 68, -8, -31, 80, -16, 11, -13, 42, 35, -86, -4, -68, 60, -23, -95, 7, 21, 86, 15, 4, 54, 3, 102, -9, -41, -108, 77, 19, -33, 43, 21, -96, -52, 12, -22, 8, 66, 13, -1, 17, 36, -65, -10, 43, 70, -36, -35, 16, -14, 124, -63, 46, 9, 62, 118, 14, 44, 9, 72, 13, 28, -42, -49, -20, 42, -23, -40, 37, 2, 18, -47, -177, 1, 101, -35, 86, -62, 54, -12, 48, -39, -60, 17, 11, -37, -61, 72, 94, -88, -12, -7, 153, 14, 37, 33, -91, 23, -68, 16, 22, 28, -42, 16, -2, -16, -3, -17, 40, -78, 35, 104, 45, -62, -74, -24, 61, -20, -23, -56, 104, -4, -138, -48, 6, -98, 60, -78, -8, 4, -27, 10, -76, -50, 13, -82, -2, -76, -51, -14, -45, 10, -96, 6, -120, 80, 2, -19, 10, 43, 82, 24, 53, -48, 69, -168, 28, 8, 22, -157, 35, 17, 142, 31, -94, -3, 68, 39, 26, 17, 22, -33, -75, 4, -12, -6, -110, -96, -45, -104, -77, -8, 17, 72, 13, -47, -112, 46, -188, -40, 32, 53, 17, 28, 2, -117, -13, 24, -40, -28, -16, -78, -38, 70, -82, 3, -130, 87, 174, -5, -34, -35, 34, -100, -24, 140, -81, -26, -28, 66, -132, 14, -29, 23, 92, 97, -1, 14, -89, 9, -54, -3, -56, -66, 73, -45, -51, 30, -32, -87, -17, 84, -20, 0, 38, 35, -31, -36, -16, 13, -27, -52, -82, 76, -52, -180, 10, 44, -35, -64, -9, 32, 29, 16, -39, -10, 12, 109, 20, -86, 164, -4, 29, 54, 76, -123, 42, 2, -4, 28, 88, 30, -76, -29, 92, 0, 29, 6, -41, 28, -73, 65, -11, -9, -11, -48, 10, 183, -52, 73, -4, 1, -58, -82, 83, 112, -39, 176, 3, 58, -99, -4, -80, -38, -11, -23, 3, 88, 288, 14, 8, -26, -17, 22, -20, 9, 88, -27, -2, 192, -77, -8, 40, 7, 5, 132, -46, 68, -25, -96, 102, -106, 52, 49, 108, 18, 2, 10, -2, 41, -3, 114, -7, -14, 219, 22, 6, -81, 100, -24, -12, -29, 8, -20, 40, -109, 146, 8, 153, -43, 14, 62, 32, 0, 116, 12, 9, -12, 55, 28, 27, -36, -89, -111, -74, -8, 32, 101, -13, -56, -52, -45, 81, -60, -18, 8, -3, 68, -5, 20, -82, 70, -38, 43, 4, -99, -4, 24, 88, 68, 0, -50, -14, -12, 61, -89, 67, -52, 8, 64, -82, 46, 111, -141, -13, 21, 16, 8, 58, 126, 44, -50, -29, 17, -75, 97, -26, 26, 119, -30, -65, -30, -54, -12, 137, 20, 15, 6, -41, 177, -8, 56, -48, -138, -121, -49, -56, -55, 92, -72, 101, 46], "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, 11, 3, 1, 5, 0]], "char_orbit_index": 7, "prim_orbit_index": 3, "minimal_twist": "187.2.g.e", "char_is_minimal": true, "conrey_index": 69, "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, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 1, 0, 0], [0, 0, -1, 1, -1, 0, 0, -1], [1, 1, 0, 0, 1, -1, -1, 0], [-1, 0, -1, 0, -1, 1, 1, -1], [1, 0, 0, 0, 0, 0, 0, 1], [0, -1, 0, 1, 0, 1, 1, 0], [0, 1, 1, 1, -1, 0, -1, 1], [1, 0, -1, -1, 0, 0, 1, 0], [1, 1, 1, 0, 0, -1, 0, 0], [1, 0, 0, -3, -1, 0, 0, 1], [0, -1, -1, 2, 0, 0, 0, -2], [0, 4, 3, 0, 1, -4, -3, 1], [0, 2, 0, -1, 1, 0, -2, -1], [-2, 0, 0, -1, -2, 1, 1, 0], [2, 0, 1, 0, 1, -1, -2, 2], [0, 0, 0, 0, -1, 0, 0, 0], [0, -2, 0, 1, 0, 2, 2, 0], [0, -2, 3, -2, 2, 0, 2, 2], [-2, -2, -2, 2, -3, 2, 2, -3], [1, 0, 0, 0, 0, -1, 0, 0], [0, -5, -2, 0, 0, 3, 3, 0], [-4, 0, 0, 4, 0, -4, 0, -4], [-1, 2, 1, 1, 1, -2, -1, 1], [0, 0, 1, -2, 2, 0, 0, -1], [-4, -3, 0, 5, -4, 1, 1, 0], [2, 0, -1, 0, 1, 1, -3, 2], [2, 0, 2, 0, 0, -2, 1, 2], [4, -2, 0, -4, 4, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, -1], [3, 3, 0, -3, 1, -3, 0, 1], [-4, 0, 0, 1, 0, 2, 0, -1], [-1, 2, 0, -2, -1, 2, -1, 3], [0, -1, -1, 0, 0, 1, 0, 0], [1, 1, -1, -1, 0, -1, 1, 0], [0, 1, -2, 0, 0, 0, -1, -2], [-3, -3, 0, -1, -3, 4, 4, 0], [-5, 0, -2, 0, 2, 2, -1, -5], [0, 0, 1, 0, 5, -1, -1, 0], [2, 1, 0, 0, 2, 0, 0, 0], [0, 0, 2, -5, 5, 0, 0, 4], [-1, -2, -1, 1, 0, 2, 1, 0], [3, -1, -1, -2, 0, -1, 0, 2], [-2, 3, -2, -1, -3, 0, -1, -3], [-2, -1, -1, -1, 0, 1, 0, 1], [-4, 4, 0, 4, 0, -4, 0, 0], [0, 7, 2, 1, -1, 0, -7, 4], [2, 1, 0, 3, 2, -2, -2, 0], [-1, 0, -3, 0, -5, 3, 0, -1], [-1, 0, 3, 0, 0, -3, 1, -1], [-1, 1, 0, 0, -1, 0, 0, 0], [0, 4, 0, -5, 5, 0, -4, 1], [-3, -1, -4, 3, 0, 1, 4, 0], [5, 0, 0, -4, 0, -1, 0, 4], [0, 1, 3, -1, 4, 0, -4, 3], [-1, 0, 0, 1, 0, 3, 0, -1], [7, 0, 2, -7, 7, 0, -2, 7], [0, -4, 2, -2, 2, 0, 4, 0], [-6, 1, 0, 7, -6, -4, -4, 0], [-3, 0, -1, 0, -6, 1, 3, -3], [-3, 0, -3, 0, 0, 3, 1, -3], [-3, -8, 0, 6, -3, 6, 6, 0], [0, -3, -1, 1, -1, 0, 3, 1], [0, 9, 7, 0, 2, -9, -7, 2], [0, -2, -2, 4, 0, 3, 0, -4], [3, 0, 0, -1, -2, 0, 0, 1], [-3, 2, 2, 1, 0, -1, 0, -1], [0, 1, 0, 0, -1, -1, 0, -1], [0, -4, 0, 0, 0, 0, 4, -8], [-1, -3, 0, 3, -1, 3, 3, 0], [-4, 0, -3, 0, -11, 3, 0, -4], [3, 0, -1, 0, 1, 1, 2, 3], [7, -1, 0, 0, 7, 0, 0, 0], [0, 3, -2, -3, 3, 0, -3, -4], [3, -3, -1, -3, 2, 3, 1, 2], [5, 5, 5, -7, 0, -5, 0, 7], [-2, -3, 2, 2, -4, 0, 1, -1], [-1, 4, 4, 0, 0, -5, 0, 0], [-4, -7, -8, 4, -9, 7, 8, -9], [0, 0, -1, 3, -3, 0, 0, -6], [3, 1, 0, 3, 3, -5, -5, 0], [-2, 0, 1, 0, 0, -1, 3, -2], [4, 0, 5, 0, -3, -5, -3, 4], [2, 2, 0, -1, 2, -2, -2, 0], [0, 1, 1, -1, 1, 0, -1, 1], [0, -6, -4, 0, 1, 6, 4, 1], [6, -4, -4, 0, 0, 4, 0, 0], [3, -2, -3, 2, -3, -1, -1, 3], [2, 3, 3, 5, 0, -7, 0, -5], [2, 2, -1, -2, 1, -2, 1, 1], [0, -2, 5, 3, -3, 0, 2, 2], [4, -4, 0, 0, 4, 0, 0, 0], [-2, 0, -2, 0, -1, 2, -1, -2], [5, 0, 2, 0, -7, -2, -3, 5], [5, 3, 0, 0, 5, -4, -4, 0], [0, -1, 3, -3, 3, 0, 1, 4], [6, -5, 0, -6, 9, 5, 0, 9], [6, -1, -1, -3, 0, 0, 0, 3], [3, 4, 4, -5, 3, -1, -3, 2], [-1, -2, -2, 0, 0, 4, 0, 0]]}