# Stored data for newform 471.2.a.d, downloaded from the LMFDB on 02 May 2024.
{"label": "471.2.a.d", "space_label": "471.2.a", "level": 471, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13510798915666391, "dim": 9, "is_polredabs": true, "trace_hash": 93999010221651776, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-1, 14, 45, -49, -53, 39, 19, -11, -2, 1]]], "qexp_display": "q+\\beta _{1}q^{2}-q^{3}+(1+\\beta _{2})q^{4}+(1+\\beta _{5}+\\cdots)q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1884, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 3.760953935202306, "hecke_ring_index": 1, "level_radical": 471, "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": "0.006", "prec": 17}, "analytic_rank_proved": true, "char_values": [471, 1, [158, 319], [1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [3, 157], "conrey_indexes": [1], "field_disc": 24147949586752, "field_disc_factorization": [[2, 6], [530359, 1], [711427, 1]], "field_poly": [-1, 14, 45, -49, -53, 39, 19, -11, -2, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.090", "prec": 17}, {"__RealLiteral__": 0, "data": "8.012", "prec": 17}, {"__RealLiteral__": 0, "data": "1.723", "prec": 17}, {"__RealLiteral__": 0, "data": "180.128", "prec": 24}, {"__RealLiteral__": 0, "data": "106.378", "prec": 24}, {"__RealLiteral__": 0, "data": "6499.618", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 9, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, 1], [157, -1]], "trace_display": [2, -9, 8, -2], "traces": [0, 9, 2, -9, 8, 8, -2, -2, 9, 9, 3, 7, -8, -1, 11, -8, 6, 20, 2, 2, 23, 2, -7, 8, -9, 17, 11, -9, -5, 19, -3, 5, 20, -7, 13, 24, 8, -8, 16, 1, 6, 42, -11, -34, 2, 8, -9, 3, -6, 27, -23, -20, -18, 16, -2, 1, -14, -2, -36, -6, -23, 14, 5, -2, 5, 23, 7, -37, 17, -8, -59, -21, 9, 23, 2, -17, -26, 15, -11, -36, 5, 9, 11, -3, 5, -20, -48, -19, -77, 27, 3, 5, -47, -5, -28, -12, -20, -2, -67, 7, 11, 35, -13, -21, -37, -24, -24, 11, -8, 3, -51, 8, -39, 4, -16, -18, -51, -1, 16, 18, -6, 24, -45, -42, 28, 42, 11, -41, 14, 34, -23, 70, -2, -10, 37, -8, 32, 26, 9, 6, -37, -3, 1, 15, 6, 49, -17, -27, -20, 59, 23, -23, -24, 20, 61, 13, 18, 9, -25, -16, 57, 48, 2, -1, 73, -1, -41, -1, 14, 38, 9, 2, -18, 33, 36, 0, -63, 6, 9, 6, 23, 43, -27, -14, 20, 8, -5, -33, -5, 2, 44, 4, -5, -6, 47, -23, -21, -10, -7, 34, 23, 37, 8, -11, -17, 12, -89, 8, -9, 36, 59, -36, 50, 21, -25, -14, -9, -31, -52, -23, 24, -39, -2, -44, -9, 17, 117, -3, 26, 51, -67, -15, -105, 27, 11, -29, -62, 36, 123, 28, -5, 55, -24, -9, 93, -64, -11, -16, 35, 3, 23, -23, -5, -5, 66, 20, 0, -2, 48, -78, -66, 19, 48, 40, 77, 72, -8, -27, 18, -11, -3, 7, -1, -5, 34, -12, 47, -32, 44, 5, 88, -15, 28, -16, -66, 12, 32, -6, 20, 61, -48, 2, 38, 12, 67, -54, -54, -7, 63, 33, -11, -22, -8, -35, 84, -18, 13, -68, -18, 21, 97, 12, 37, -35, 2, 24, -19, -12, 24, 56, 28, -11, -61, -50, 8, -30, 31, -3, 148, -13, 51, -15, -30, -8, 182, -51, 39, -18, 72, -4, -45, -53, 16, 26, -110, 18, 39, -31, 51, 36, -108, 1, 16, -7, -16, -43, -24, -18, -73, 3, 6, -23, -112, -24, 108, -101, 45, 52, -69, 42, 76, -64, -28, -73, 61, -42, -53, 6, -11, -69, 52, 41, 28, -2, -14, -51, -23, -34, 149, -63, 23, 8, -13, -70, 99, 50, 2, -75, 81, 10, -145, -42, -37, -165, 65, 8, 30, -36, -32, 19, -33, -26, -180, -102, -9, 11, -128, -6, 6, 2, 37, 3, 21, 3, 82, -62, -1, -132, 28, -15, -80, -60, -6, 35, 33, -49, -43, -28, 17, -4, -95, 27, 81, 62, 20, 63, -59, -59, 12, 24, -23, 9, 41, 23, -84, -77, 24, -123, 65, -20, -71, -71, -61, -31, 8, -13, -92, -68, -18, 31, -174, -9, -6, -28, 25, -84, -13, 16, 19, -21, -57, 116, -30, -48, -43, 106, -2, -56, 106, 1, -104, 72, -73, 1, -162, 1, 117, -41, 41, 38, -45, 1, -13, 16, -14, 1, 131, -38, 13, -84, -9, -87, -39, -2, 14, -91, 18, 26, 56, -33, -93, 102, -36, 22, 262, 0, -141, 65, 63, -1, -82, -6, -58, -77, -9, 95, -73, -6, -37, 110, -23, 12, -1, -43, -51, 127, 27, -137, 146, 14, 8, 128, -20, 92, -13, -8, -54, -98, 5, -8, -169, 33, -29, -8, 5, -16, -241, -2, -41, -19, -44, 50, 95, -4, -15, 58, 5, 33, 77, 6, 37, 5, -47, -66, 127, 23, 70, 48, 21, 92, 176, 10, 10, 92, 7, 8, 82, -34, 95, 86, -23, 64, 104, -37, -43, 11, -8, 76, 94, 11, -81, 176, 17, -4, 104, -12, 63, 59, 89, -23, 120, -8, -109, 89, 9, 89, -77, -36, 8, -2, -59, 156, 64, 36, 50, 25, -50, -212, -39, -21, 139, 12, 25, -38, 201, 14, -60, -58, 9, 0, 122, 31, -20, 28, 52, 4, 169, 23, 140, 23, -24, 96, 94, 39, -255, -126, 2, -53, -7, 44, -67, 61, 9, 42, 11, -17, -19, 22, -117, 12, -48, 3, -100, 94, -26, -40, 33, -51, -36, 90, 67, 68, 24, 15, -1, -46, 105, 54, 59, -27, 24, -45, -11, -12, -95, 29, 36, -55, 62, 14, 109, -36, 59, -169, -123, 3, -93, -28, 92, 51, 5, 131, 70, -55, 1, -8, 24, 37, 237, 9, 5, 42, -93, -85, 125, 64, -91, 111, 11, -113, -76, 16, -78, 163, -35, 33, -53, -3, 126, 25, -23, -42, -6, 23, -121, -95, 5, 4, 122, 5, 98, 3, -66, 61, -8, -20, 198, 8, 0, 90, 97, 2, -17, 0, -48, -20, -46, 78, -158, 44, 66, -105, 87, -19, -189, 8, -48, -117, 341, -40, -179, 26, -77, 7, -25, -72, 121, 27, 8, 107, 47, 27, -10, -5, -18, 286, -242, 11, 11, 25, 3, 26, -153, -7, -6, -11, 1, -52, -22, 5, 221, -38, -34, -9, -73, 12, -28, 72, -47, -35, -57, 32, -251, 66, -44, -105, -170, -5, 97, -61, -88, 138, -37, 15, -157, -169, -28, 5, 212, 16, -138, -112, 66, 7, 5, -12, 25, 115, -32, 26, -126, 6, -29, -30, -20, 169, 91, -61, -268, -125, 48, 123, -147, -2, -28, 232, -38, 73, 121, -12, -231, 14, -67, -142, 160, 54, 88, 83, 54, -61, -101, 7, 55, -106, -63, 20, -137, -33, 161, 156, 11, -44, -145, 22, 164, -63, 8, -147, 1, 35, 213, -82, -84, 189, 125, 18, 4, -20, -13, 51, 16, 68, -7, 35, 18, -38, 60, -21, 63, -83, -97, -16, -99, -12, -74, -51, -37, -6, 25, 35, -143, -132, -2, 96, 34, -24, -82, 39, 19, -129, 160, 12, -118, 62, -24, 110, 105, -56, -44, -100, -28, 80, 94, 11, 55, -130, 61, 49, -128, 50, 15, 52, -8, -150, -69, 30, 89, -52, -31, 5, 54, 3, -133, 29, -148, 178, -178, 13, -198, -190, -51, -39, 214, 15, 57, 316, 30, 54, 11, 8, -104], "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": "471.2.a.d", "char_is_minimal": true, "conrey_index": 1, "id": null, "nf_label": 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, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0], [-1, 1, -1, -1, -1, 1, -1, 0, -1], [2, 0, 1, 0, 1, -1, -1, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 1, -1, 1, 0, 1], [-1, 1, -1, -1, -2, 1, 0, -1, 0], [-1, 0, -1, 0, 0, 0, 0, 0, 0], [-1, 1, -1, -1, 0, 1, 0, -1, 0], [1, -1, 1, 1, 0, -1, 2, -1, 0], [-1, 0, 0, 0, 0, -1, 0, 0, 0], [2, 0, 1, 0, 2, -1, 1, 2, 1], [3, -1, 1, 1, 1, -1, 1, 0, -1], [0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 0, 0, 0, 1, 1, 1], [3, 0, 1, 0, 0, 0, 0, 1, 1], [1, -1, 1, 1, 1, -1, 1, 0, 1], [-2, 2, -2, 0, -1, 0, -1, -1, -1], [0, 1, -2, -2, -1, 0, -3, 0, -1], [-2, 0, -1, 0, -1, 1, 1, -1, 0], [2, 0, 0, 1, -1, 1, -2, -1, 0], [0, 0, 0, 0, -1, 0, -1, -3, -1], [-1, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 2, -2, -2, -1, 0, -3, -1, -1], [3, -2, -1, 1, 1, 1, 3, 1, 1], [-1, -1, -1, -2, -1, 1, -1, 0, -1], [3, -2, 2, 3, 2, -1, 3, 2, 1], [3, 0, 1, 0, 0, 0, 0, 2, 1], [1, -1, 1, 1, 2, -1, 0, 1, 0], [-1, 3, -1, -3, -2, 1, -2, -1, -2], [3, -1, -1, -1, -1, -1, -5, 0, -1], [1, 0, 1, 0, 0, 0, 0, 0, 0], [0, -1, 1, 2, 2, 0, 3, -1, 1], [3, -1, 0, 1, 0, 0, 0, 2, 1], [1, -1, 1, 1, 0, -1, 0, 1, 0], [2, 1, 0, -2, 1, 0, -2, 4, 0], [5, 0, 0, -2, 0, -1, -2, 2, 0], [-1, 1, -1, -1, 0, 1, -2, 1, 0], [-2, -4, 2, 2, 2, 0, 4, 0, 0], [1, -5, 1, 1, 1, 1, 3, -2, -1], [1, 0, 0, 0, 0, 1, 0, 0, 0], [-2, -2, 1, 0, 0, 0, 4, -2, 0], [0, -2, 0, -2, 1, 0, 1, -1, -1], [-2, 0, -1, 0, -2, 1, -1, -2, -1], [2, -1, -1, -1, -3, -1, -3, 0, -1], [-2, 1, 1, 4, 2, 1, 6, -1, 3], [-3, 1, -1, -1, -1, 1, -1, 0, 1], [-5, 1, -1, -1, -3, 1, -1, -4, -3], [4, -3, 1, -1, 3, 0, 1, 2, 1], [0, -1, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 1, 1, -2, 1, 0, -3, 0], [-3, -1, -1, -3, -1, 3, -1, -2, -1], [0, -1, 1, 0, 0, 0, -1, -1, -1], [-4, 2, -3, 2, -1, 0, -1, 1, 1], [-1, 2, -1, 1, 0, -1, 0, 0, 2], [-3, 0, -1, 0, 0, 0, 0, -1, -1], [1, -1, 1, -3, -1, -1, -3, 0, 1], [3, 1, 0, 1, 1, 0, -1, 5, 2], [-1, 1, -1, -1, -1, 1, -1, 0, -1], [2, 2, 1, 3, 0, -1, -1, 2, 1], [3, -1, 1, 5, 0, -1, 2, -3, 0], [2, -2, 2, 0, 1, 0, 1, 1, 1], [-7, 3, -1, -3, -2, 1, 0, -1, 0], [-2, 4, 0, -4, -3, 0, -3, -3, -1], [0, -1, 2, 2, 1, 0, 3, 0, 1], [-7, -1, 1, 1, 2, 1, 8, -1, 2], [-1, -1, 1, 3, 2, -1, 2, -1, 0], [2, 0, 1, 0, 1, -1, -1, 1, 0], [3, -1, 1, -1, 0, -3, -2, 1, 0], [-1, 1, -2, -1, -2, 2, -4, -2, -1], [-2, 0, 0, -1, 1, -1, 2, 1, 0], [1, -2, 3, 4, 3, -1, 2, 3, 2], [1, 3, -1, 1, -2, -1, -2, 1, -2], [0, 0, 0, 0, 1, 0, 1, 3, 1], [-3, -1, -1, -3, 1, 1, -3, 2, -1], [6, -3, 6, 4, 6, -6, 4, 5, 2], [1, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 0, 3, -3, 1, 4, 1], [-2, -1, 0, 2, -2, 2, 4, -3, 0], [2, -2, 2, 2, 1, 0, 3, 1, 1], [-1, -1, -1, -1, 3, 1, 3, 2, 1], [-6, 0, -4, -2, -2, 0, -6, 0, -2], [-3, 2, 1, -1, -1, -1, -3, -1, -1], [-11, 1, -3, -3, -2, 1, -4, -3, -2], [3, 1, -3, -3, 0, 1, -2, 3, 0], [1, 1, 1, 2, 1, -1, 1, 0, 1], [5, -5, 7, 5, 4, -5, 0, -1, 0], [-8, 3, -3, -2, -3, 1, -5, -3, -4], [-3, 2, -2, -3, -2, 1, -3, -2, -1], [-7, 3, -3, -5, -3, -1, -7, -4, -5], [1, -1, 4, 4, 3, -3, 3, 0, 1], [-3, 0, -1, 0, 0, 0, 0, -2, -1], [-3, 3, 1, -1, -3, 3, 1, -2, 1], [-9, 2, -3, -1, 0, 1, 4, 1, 0], [-1, 1, -1, -1, -2, 1, 0, -1, 0], [2, 0, -2, 0, 0, 1, -1, 2, 1]]}