# Stored data for newform 503.2.a.d, downloaded from the LMFDB on 25 April 2024.
{"label": "503.2.a.d", "space_label": "503.2.a", "level": 503, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13510798915666423, "dim": 3, "is_polredabs": true, "nf_label": "3.3.257.1", "trace_hash": 1314849374173196371, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [3, -5, 0, 1]], [3, [3, -4, -1, 1]]], "qexp_display": "q+\\beta _{2}q^{2}+\\beta _{1}q^{3}+(1+\\beta _{1}-\\beta _{2})q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2012, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 4.016475221670404, "hecke_ring_index": 1, "level_radical": 503, "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": "0.010", "prec": 17}, "analytic_rank_proved": true, "char_values": [503, 1, [5], [1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [503], "conrey_indexes": [1], "field_disc": 257, "field_disc_factorization": [[257, 1]], "field_poly": [3, -4, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.035", "prec": 17}, {"__RealLiteral__": 0, "data": "2.787", "prec": 17}, {"__RealLiteral__": 0, "data": "0.445", "prec": 17}, {"__RealLiteral__": 0, "data": "21.016", "prec": 20}, {"__RealLiteral__": 0, "data": "9.018", "prec": 17}, {"__RealLiteral__": 0, "data": "241.368", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[503, -1]], "trace_display": [0, 1, 0, 1], "traces": [0, 3, 0, 1, 4, 0, 1, 1, -9, 0, 0, 11, 9, 5, -9, 0, 2, 12, 10, 12, 0, 8, -1, -12, -2, -15, -11, -2, 18, -2, 0, -10, -3, -5, 20, 0, -9, 2, 0, -8, 0, 2, -1, 5, 7, 0, 0, 19, -10, -4, 0, 6, 8, 14, 8, 0, -12, 4, -22, -5, 0, 6, -18, -9, -7, 0, -6, 35, -2, -4, 0, 12, 10, 35, -4, -5, 16, -4, -19, -7, 0, -17, 42, -1, 3, 0, -28, -20, -34, 4, 0, 3, -16, 12, -12, 0, -27, -23, -21, -1, -20, -20, 26, 2, -26, 0, -24, -8, -27, 14, 0, -34, 11, 1, 4, 0, 0, -11, -12, -14, 0, 16, 0, 22, 20, 0, 20, 16, 15, 16, 0, -5, 33, 4, -8, 0, -16, 36, -4, 4, 0, -12, -20, 28, -21, 0, 19, -12, -28, 18, -5, -16, -36, 20, -35, 0, 15, 14, 35, -32, 0, -4, -39, -10, -18, 0, 9, -14, -25, -10, 0, 0, 49, 7, -42, -5, 18, -20, 24, -50, 0, 14, -37, 2, 36, 0, -6, 42, 19, -25, 0, -22, -10, 32, 25, 0, 5, -14, 29, 19, 45, 28, -16, 2, 36, 0, -32, 0, 35, 44, 0, -26, 6, 2, 4, 0, 14, 30, 62, 5, 0, -2, -38, -45, -24, 0, 22, 2, 36, 3, 0, 38, -16, -5, 18, 0, -13, 44, 4, -32, 0, 4, 2, 5, 8, 0, 64, 20, 12, -8, 0, 0, -30, -44, 78, 0, -20, 3, -12, -30, 0, -22, 28, -1, 9, 0, -36, 38, 71, -10, 0, -15, -34, 23, 20, -55, -36, 12, -8, -18, 0, -2, -24, -5, 34, 0, -25, -20, -3, 37, 0, -48, 21, -3, -33, 0, -10, 9, -20, -20, -45, 44, 30, 26, 8, 0, 22, -22, 69, 66, 0, 56, 5, -38, 22, 0, 2, -53, -56, 12, 0, 32, 36, 48, 21, -25, 2, 28, 36, 0, 0, 18, -18, -4, 4, 0, 16, 26, -21, -66, 0, -52, 40, 2, -43, 0, -53, -22, -6, -30, 45, 5, 15, -18, -32, 0, 18, 30, 18, -24, 0, -9, -64, -63, 63, 0, 2, -19, -8, 42, 0, -8, -30, 45, 54, 0, -69, 38, 22, 71, 0, -4, 42, -43, 53, 0, -64, -28, -96, -29, 0, -48, -9, -16, 32, 0, -36, 13, 47, 32, -10, 45, 20, -14, 22, 0, -38, 42, 8, 36, 0, 14, 100, -8, -40, 0, 24, -68, -4, -6, 0, 65, 24, -12, -66, -60, -18, 2, 20, -36, 0, -28, -1, 3, -6, 0, -20, -48, 24, 20, 0, -21, -8, -47, 6, 0, 3, 4, -19, -30, -50, -14, -87, -88, -44, 0, -8, 34, 90, 8, 0, -44, 3, 32, 62, 0, -65, 12, -48, 36, 0, 24, 3, 4, 79, -60, 12, -24, 38, -54, 0, 42, -16, -32, -49, 0, -64, -84, -18, 14, 0, 32, 6, -52, -44, 0, 14, 22, 1, -10, 0, 30, -40, 3, 47, 0, 4, -14, -66, 37, 0, -14, 84, -8, 59, 0, 15, 88, -14, 57, 0, -41, -4, -22, -49, -40, -71, -76, -25, -21, 0, -12, 72, -60, 62, 0, -113, -32, -32, -4, 0, -8, 84, -36, -18, 0, -14, -19, 30, 0, 5, -8, 8, 9, 40, 0, -56, 25, 0, 22, 0, -32, 84, 12, 57, 0, 28, 38, -56, 93, 0, 10, 17, 14, 78, 60, 9, -40, 124, -30, 0, -17, -23, 88, -86, 0, -10, 15, -12, -40, 0, -70, 44, -46, 41, 0, 42, 71, 44, -25, 10, 41, -71, -8, -134, 0, 10, -101, -12, 14, 0, 62, 24, 0, 50, 0, -23, -80, 34, -2, 0, 8, -58, 14, 26, 75, -56, -20, 16, 0, 0, -25, 56, 28, -26, 0, 42, 25, -46, -20, 0, 57, 36, 26, -72, 0, 80, 8, 12, 0, 55, -42, 2, 1, 90, 0, -104, 19, -81, -31, 0, -23, 40, -70, 12, 0, -24, 8, 12, 11, 0, 22, 18, 21, 136, 10, -3, -64, -44, -73, 0, -38, -66, 50, -36, 0, 33, 10, 45, 84, 0, -31, 117, -35, 8, 0, 18, 92, 34, -51, -90, 25, 56, 8, -18, 0, -20, 42, -15, -28, 0, 35, 12, 40, 34, 0, -100, -24, 34, -37, 0, 98, 0, 34, 42, 10, -61, 45, -46, 12, 0, -36, 18, 42, -35, 0, 12, 112, -14, -39, 0, -32, -90, -24, -42, 0, 57, 9, -44, 28, 0, -8, 55, -4, 2, 0, -36, 70, 49, 20, 0, -29, 74, -34, -50, 0, -148, 22, 39, -14, 0, 84, 66, -10, 59, 50, 94, 40, -29, 8, 0, 46, -80, 18, 50, 0, 12, -70, -116, -16, 0, -88, 32, 10, 114, 0, 43, 1, -4, 52, 15, 24, -59, 135, 105, 0, -30, 62, 44, -30, 0, -20, 54, -48, 22, 0, -102, 20, -94, -37, 0, -82, 34, -44, -38, 25, -9, 68, 36, -18, 0, 8, -13, -58, -76, 0, 28, -42, 48, 103, 0, -3, -14, 42, -22, 0, 57, -65, 94, -16, -100, -8, 36, -7, -18, 0, 28, 57, -61, -42, 0, -16, -70, -70, 51, 0, -98, 59, -6, -72, 0, 50, 20, 25, 0, 0, 105, 32, -78, -2, 0, 17, -3, 63, -64, 0, -21, -45, 64, -82, 0, -67, -37, 76, -16, 0, 87, 32, 6, 12, 45, 8, 104, -1, 19, 0, -58, 80, 8, -16, 0, 56, -40, 4, -76, 0, -77, -44, -30, 31, 0, -88, 18, 42, -12, -10, 48, -32, 60, -54, 0, -16, 9, 30, -6, 0, 51, 6, -121, 16, 0, 49, 46, -8, 39, 0, -100, 56, -21, 46, 0, 14, 46, 65, 34, 0, -94, -52, -26, -6, 0, 7, 54, 4, 54, 0, 4, -70, -46, 24, 0, -92, 30, -60, -80, 40, 4, 11, 16, -22, 0, 62, -46, 14, -2, 0, -96, 69, 32, -20, 0, 37, -36, 10, -76, 0, -3, 16, -124, 64, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": true, "level_is_prime_power": true, "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": "503.2.a.d", "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], [0, 0, 1], [0, 1, 0], [1, 1, -1], [0, 0, 0], [0, 1, 1], [0, 1, -1], [-3, 0, 1], [0, 0, 1], [0, 0, 0], [4, -1, 0], [3, 0, 0], [2, -1, -1], [-3, 0, 2], [0, 0, 0], [1, -1, -2], [4, 0, 2], [3, 1, -1], [4, 0, 0], [0, 0, 0], [3, -1, 0], [0, -1, 3], [-4, 0, 0], [0, -2, 1], [-5, 0, 0], [-3, -2, 2], [0, -2, 1], [6, 0, -3], [0, -2, -2], [0, 0, 0], [-4, 2, -2], [0, -3, 0], [-3, 4, -1], [6, 2, 2], [0, 0, 0], [-3, 0, 3], [2, -4, 0], [0, 0, 4], [-3, 1, -2], [0, 0, 0], [0, 2, 4], [0, -1, 2], [1, 2, -3], [1, 4, -4], [0, 0, 0], [0, 0, -4], [7, -2, -1], [-3, -1, -3], [-1, -1, -2], [0, 0, -5], [0, 6, 2], [2, 2, -5], [6, -4, -2], [3, -1, -3], [0, 0, 0], [-3, -3, 5], [0, 4, 0], [-6, -4, 0], [-1, -2, -1], [0, 0, 0], [2, 0, 0], [-6, 0, 0], [-3, 0, 2], [-2, -1, 1], [0, 0, 0], [-3, 3, 2], [11, 2, -1], [-2, 4, 2], [0, -4, 0], [0, 0, 0], [4, 0, -2], [3, 1, -4], [12, -1, 2], [0, -4, -2], [0, -5, 0], [4, 4, -4], [-3, 5, -4], [-6, -1, 0], [-4, 5, 3], [0, 0, 0], [-6, 1, -4], [12, 6, -2], [0, -1, 1], [0, 3, -3], [0, 0, 0], [-9, -1, 6], [-6, -2, -4], [-12, 2, 3], [0, 4, 2], [0, 0, 0], [0, 3, -4], [-4, -4, 4], [6, -6, 0], [-3, -3, 6], [0, 0, 0], [-9, 0, -3], [-6, -5, 3], [-6, -3, 0], [0, -1, 3], [-5, -5, 5]]}