# Stored data for newform 504.2.r.e, downloaded from the LMFDB on 25 April 2024.
{"label": "504.2.r.e", "space_label": "504.2.r", "level": 504, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18015566774141432, "dim": 8, "is_polredabs": true, "nf_label": "8.0.2091141441.1", "trace_hash": 1409236919273133241, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [4, 18, 65, 84, 93, -6, 17, 3, 1]]], "qexp_display": "q+\\beta _{4}q^{3}+(\\beta _{2}+\\beta _{4}+\\beta _{6})q^{5}+(1+\\beta _{2}+\\cdots)q^{7}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "r", "char_is_real": false, "Nk2": 2016, "analytic_conductor": 4.024460261872531, "hecke_ring_index": 3, "level_radical": 42, "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": "0.005", "prec": 17}, "analytic_rank_proved": true, "char_values": [504, 3, [127, 253, 281, 73], [3, 3, 2, 3]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [169, 337], "field_disc": 2091141441, "field_disc_factorization": [[3, 4], [5081, 2]], "field_poly": [81, -27, 9, 9, -15, 3, 1, -1, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.025", "prec": 17}, {"__RealLiteral__": 0, "data": "7.345", "prec": 17}, {"__RealLiteral__": 0, "data": "0.724", "prec": 17}, {"__RealLiteral__": 0, "data": "225.133", "prec": 24}, {"__RealLiteral__": 0, "data": "82.792", "prec": 20}, {"__RealLiteral__": 0, "data": "13051.366", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c3", "trace_display": [0, -1, -3, 4], "traces": [0, 8, 0, -1, 0, -3, 0, 4, 0, -1, 0, 7, 0, 3, 0, -11, 0, 6, 0, -8, 0, 1, 0, 2, 0, -5, 0, 11, 0, -9, 0, 3, 0, -21, 0, -6, 0, 6, 0, 2, 0, 9, 0, 8, 0, 7, 0, 3, 0, -4, 0, -18, 0, 12, 0, -56, 0, 34, 0, 10, 0, 20, 0, -2, 0, 1, 0, 11, 0, -17, 0, -6, 0, -48, 0, 52, 0, -7, 0, 21, 0, -25, 0, 8, 0, 9, 0, -15, 0, 12, 0, 6, 0, 29, 0, 36, 0, 16, 0, 18, 0, -7, 0, 8, 0, 11, 0, -80, 0, -62, 0, -11, 0, -10, 0, 13, 0, -52, 0, 3, 0, 9, 0, -35, 0, 84, 0, -12, 0, 3, 0, -29, 0, -4, 0, -38, 0, 16, 0, 48, 0, -31, 0, 8, 0, -12, 0, 2, 0, -18, 0, 37, 0, 3, 0, 7, 0, 29, 0, -24, 0, 4, 0, 20, 0, 51, 0, 9, 0, 21, 0, -5, 0, -31, 0, 5, 0, 29, 0, -38, 0, -86, 0, 19, 0, -25, 0, -6, 0, -8, 0, 9, 0, 28, 0, -68, 0, 22, 0, -24, 0, 48, 0, 9, 0, 2, 0, 40, 0, -40, 0, -3, 0, -22, 0, -10, 0, 6, 0, 64, 0, -30, 0, 37, 0, -101, 0, 14, 0, 1, 0, -9, 0, 40, 0, -68, 0, 1, 0, -29, 0, 21, 0, 59, 0, -3, 0, 3, 0, 35, 0, -10, 0, 30, 0, 24, 0, 51, 0, 3, 0, -45, 0, 7, 0, 57, 0, -21, 0, 30, 0, -56, 0, 4, 0, 62, 0, 24, 0, 125, 0, -12, 0, 7, 0, 5, 0, 18, 0, -10, 0, 38, 0, -61, 0, -22, 0, 9, 0, 32, 0, -8, 0, -49, 0, -2, 0, -42, 0, 87, 0, 16, 0, -8, 0, -13, 0, -62, 0, 3, 0, 35, 0, -18, 0, -108, 0, 25, 0, -3, 0, -30, 0, 13, 0, -1, 0, -34, 0, -70, 0, 20, 0, -8, 0, 17, 0, 10, 0, 50, 0, 50, 0, 1, 0, -8, 0, 12, 0, -24, 0, -12, 0, -49, 0, 26, 0, -15, 0, -122, 0, 6, 0, 35, 0, -96, 0, -138, 0, 40, 0, 1, 0, 11, 0, -28, 0, -42, 0, -11, 0, 51, 0, 45, 0, -40, 0, 86, 0, 32, 0, -29, 0, 47, 0, 61, 0, 28, 0, -7, 0, -61, 0, 20, 0, 54, 0, -74, 0, 4, 0, -29, 0, 53, 0, 66, 0, -20, 0, -27, 0, -154, 0, 56, 0, -42, 0, -41, 0, -21, 0, -1, 0, 35, 0, 42, 0, -21, 0, 42, 0, 22, 0, 65, 0, -1, 0, -64, 0, 18, 0, 6, 0, 10, 0, 103, 0, -8, 0, 22, 0, 100, 0, -13, 0, 92, 0, -105, 0, 21, 0, 1, 0, -28, 0, 44, 0, -6, 0, -101, 0, 30, 0, 75, 0, 24, 0, -3, 0, -33, 0, -58, 0, -64, 0, -84, 0, -21, 0, -40, 0, -24, 0, -83, 0, 65, 0, -37, 0, 40, 0, 60, 0, -38, 0, 17, 0, 21, 0, 30, 0, 95, 0, -56, 0, 5, 0, 99, 0, -14, 0, 66, 0, -15, 0, 12, 0, -77, 0, 67, 0, -36, 0, -21, 0, -7, 0, 250, 0, -62, 0, 54, 0, 1, 0, -78, 0, -47, 0, 10, 0, 44, 0, -2, 0, 28, 0, 70, 0, -123, 0, -8, 0, -51, 0, 64, 0, -21, 0, 18, 0, -10, 0, -82, 0, 18, 0, 30, 0, 42, 0, 85, 0, -18, 0, -92, 0, -63, 0, 15, 0, 50, 0, -82, 0, -169, 0, -7, 0, 13, 0, -56, 0, 6, 0, -122, 0, 108, 0, -18, 0, 88, 0, -120, 0, 56, 0, 3, 0, -7, 0, -55, 0, 32, 0, 24, 0, -150, 0, -24, 0, 25, 0, -46, 0, -50, 0, 43, 0, -45, 0, 13, 0, 72, 0, 72, 0, 180, 0, -88, 0, -21, 0, -36, 0, 43, 0, 67, 0, -16, 0, 108, 0, -58, 0, -154, 0, -36, 0, 24, 0, 10, 0, 6, 0, -22, 0, -12, 0, 0, 0, -52, 0, -72, 0, 91, 0, 7, 0, -30, 0, 67, 0, -25, 0, -70, 0, -18, 0, 138, 0, 16, 0, 16, 0, -78, 0, 15, 0, -61, 0, 84, 0, -89, 0, 22, 0, 20, 0, -76, 0, -80, 0, 92, 0, -30, 0, -31, 0, -40, 0, -53, 0, 40, 0, 56, 0, 228, 0, -39, 0, 36, 0, -31, 0, -66, 0, 7, 0, 96, 0, 28, 0, 254, 0, 222, 0, -22, 0, -30, 0, 5, 0, 207, 0, 154, 0, -17, 0, -1, 0, -20, 0, 212, 0, -36, 0, 18, 0, -24, 0, -33, 0, -50, 0, -13, 0, 44, 0, -126, 0, -138, 0, 83, 0, 37, 0, -47, 0, -26, 0, -107, 0, -58, 0, 81, 0, 50, 0, 22, 0, -143, 0, -3, 0, -17, 0, 26, 0, 93, 0, -61, 0, 69, 0, -84, 0, 18, 0, -141, 0, 13, 0, 7, 0, -199, 0, -16, 0, -36, 0, -28, 0, -144, 0, 142, 0, -133, 0, -41, 0, -50, 0, -73, 0, 42, 0, -50, 0, 25, 0, 30, 0, 200, 0, 67, 0, -86, 0, -6, 0, -96, 0, -63, 0, 112, 0, 67, 0, 132, 0, 138, 0, 45, 0, 37, 0, 10, 0, 179, 0, -39, 0, 19, 0, 95, 0, -58, 0, 4, 0, -224, 0, -7, 0, -57, 0, -42, 0, 47, 0, 4, 0, -45, 0, 120, 0, -124, 0, -66, 0, -85, 0, 19, 0, -55, 0, 95, 0, -5, 0, -94, 0, -218, 0, -22, 0, 102, 0, -16, 0, -33, 0, 53, 0, 46, 0, -160, 0, 3, 0, 64, 0, 96, 0, 118, 0, 48, 0, -36, 0, 4, 0, 56, 0, -46, 0, -2, 0, 162, 0, -34, 0, -175, 0, -123, 0, -40, 0, 55, 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": 18, "prim_orbit_index": 3, "minimal_twist": "504.2.r.e", "char_is_minimal": true, "conrey_index": 169, "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, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [2, -1, 2, -1, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, -3, 1, -1, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, -1, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 2, 0, 1, 1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 1, -1, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 2, -2, 3, -2, 0, -3, -2], [0, 0, 0, 0, 0, 0, 0, 0], [3, -2, 3, 0, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, -3, -1, 0, 0, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, -1, -2, 1, -2, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 1, 0, 2, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, -1, 1, -1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, -2, 2, -1, 2, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, -1, -1, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [3, -3, 3, -3, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 1, -2, 1, 0, 2, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, -1, -3, 0, 0, 1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 4, -3, 1, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-8, 4, 0, 3, 1, -2, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, -1, -3, 0, -1, 1, -1, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, -3, -3, 3, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [6, 0, 6, 1, 0, 0, -1, 3], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [1, -3, 1, -3, 3, 0, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, -4, -3, 2, 1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 3, 0, 0, 2, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 0, 0, -1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 2, 0, -1, 3, 0, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [9, -7, 3, -2, 0, 1, 2, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [5, 1, 5, -2, -1, 0, 2, 3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 6, 3, 0, 1, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 1, 2, 2, -1, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -3, 0, -2, 1, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-3, -3, -3, -3, 0, -3, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 3, -2, -1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 6, -3, -1, 1, 0, -5, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, -10, 2, -5, 3, -3, -3], [0, 0, 0, 0, 0, 0, 0, 0], [3, 2, 3, 1, -2, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [3, -2, 0, 0, -3, 2, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0]]}