# Stored data for newform 504.2.s.c, downloaded from the LMFDB on 25 April 2024.
{"label": "504.2.s.c", "space_label": "504.2.s", "level": 504, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9008436238877176, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 45027589379538303, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [1, 1, 1]], [11, [9, -3, 1]], [13, [6, 1]]], "qexp_display": "q+(-1+\\zeta_{6})q^{5}+(-3+2\\zeta_{6})q^{7}+3\\zeta_{6}q^{11}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "s", "char_is_real": false, "Nk2": 2016, "analytic_conductor": 4.024460261872531, "hecke_ring_index": 1, "level_radical": 42, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.007", "prec": 17}, "analytic_rank_proved": true, "char_values": [504, 3, [127, 253, 281, 73], [3, 3, 3, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [289, 361], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.034", "prec": 17}, {"__RealLiteral__": 0, "data": "1.953", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.334", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "100.018", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [0, 0, -1, -4], "traces": [0, 2, 0, 0, 0, -1, 0, -4, 0, 0, 0, 3, 0, -12, 0, 0, 0, -5, 0, -1, 0, 0, 0, -7, 0, 4, 0, 0, 0, -4, 0, 5, 0, 0, 0, -1, 0, -3, 0, 0, 0, 4, 0, -8, 0, 0, 0, 5, 0, 2, 0, 0, 0, -1, 0, -6, 0, 0, 0, 15, 0, 5, 0, 0, 0, 6, 0, 9, 0, 0, 0, 0, 0, -7, 0, 0, 0, -15, 0, -1, 0, 0, 0, -24, 0, 10, 0, 0, 0, 7, 0, 24, 0, 0, 0, -1, 0, -4, 0, 0, 0, 3, 0, 15, 0, 0, 0, 9, 0, 5, 0, 0, 0, 36, 0, -7, 0, 0, 0, 25, 0, 2, 0, 0, 0, -18, 0, 16, 0, 0, 0, 5, 0, -1, 0, 0, 0, 11, 0, -24, 0, 0, 0, -18, 0, 2, 0, 0, 0, -17, 0, 5, 0, 0, 0, -10, 0, 9, 0, 0, 0, -7, 0, -13, 0, 0, 0, 24, 0, 46, 0, 0, 0, -13, 0, -20, 0, 0, 0, -13, 0, -20, 0, 0, 0, -3, 0, 15, 0, 0, 0, -11, 0, -3, 0, 0, 0, 12, 0, 13, 0, 0, 0, 8, 0, -2, 0, 0, 0, -6, 0, -8, 0, 0, 0, 4, 0, -25, 0, 0, 0, 30, 0, -48, 0, 0, 0, 11, 0, -23, 0, 0, 0, 11, 0, 5, 0, 0, 0, -40, 0, 17, 0, 0, 0, 11, 0, 6, 0, 0, 0, -32, 0, -42, 0, 0, 0, -21, 0, -3, 0, 0, 0, -9, 0, 2, 0, 0, 0, -9, 0, 7, 0, 0, 0, -12, 0, 17, 0, 0, 0, -12, 0, 13, 0, 0, 0, -8, 0, -8, 0, 0, 0, -12, 0, -30, 0, 0, 0, 42, 0, 16, 0, 0, 0, 5, 0, 8, 0, 0, 0, 15, 0, 1, 0, 0, 0, 3, 0, -6, 0, 0, 0, 10, 0, -24, 0, 0, 0, 5, 0, -29, 0, 0, 0, -18, 0, -20, 0, 0, 0, -15, 0, 20, 0, 0, 0, 15, 0, 4, 0, 0, 0, 3, 0, 0, 0, 0, 0, 21, 0, 18, 0, 0, 0, 14, 0, -23, 0, 0, 0, 5, 0, -11, 0, 0, 0, 24, 0, 48, 0, 0, 0, -3, 0, 12, 0, 0, 0, -29, 0, 70, 0, 0, 0, -1, 0, 17, 0, 0, 0, 27, 0, -30, 0, 0, 0, -18, 0, -27, 0, 0, 0, -75, 0, 12, 0, 0, 0, -40, 0, 68, 0, 0, 0, 20, 0, 5, 0, 0, 0, 3, 0, -4, 0, 0, 0, -7, 0, -21, 0, 0, 0, -31, 0, 7, 0, 0, 0, 52, 0, 6, 0, 0, 0, 6, 0, 17, 0, 0, 0, 60, 0, -32, 0, 0, 0, -3, 0, -45, 0, 0, 0, -12, 0, -8, 0, 0, 0, 31, 0, 18, 0, 0, 0, 2, 0, -7, 0, 0, 0, 48, 0, 10, 0, 0, 0, 0, 0, 35, 0, 0, 0, 64, 0, -6, 0, 0, 0, -9, 0, 35, 0, 0, 0, 15, 0, 30, 0, 0, 0, -33, 0, 7, 0, 0, 0, 25, 0, -26, 0, 0, 0, -24, 0, 9, 0, 0, 0, 39, 0, 41, 0, 0, 0, -10, 0, -16, 0, 0, 0, 2, 0, -1, 0, 0, 0, -5, 0, 48, 0, 0, 0, -41, 0, -18, 0, 0, 0, -33, 0, 13, 0, 0, 0, -56, 0, 33, 0, 0, 0, 48, 0, 3, 0, 0, 0, 40, 0, -10, 0, 0, 0, -45, 0, -20, 0, 0, 0, -17, 0, 44, 0, 0, 0, 2, 0, -13, 0, 0, 0, -30, 0, -43, 0, 0, 0, -60, 0, 9, 0, 0, 0, 7, 0, -11, 0, 0, 0, 30, 0, -32, 0, 0, 0, -8, 0, -12, 0, 0, 0, -17, 0, -88, 0, 0, 0, 15, 0, -45, 0, 0, 0, 35, 0, 5, 0, 0, 0, -88, 0, -23, 0, 0, 0, 5, 0, 14, 0, 0, 0, 30, 0, -52, 0, 0, 0, 39, 0, 8, 0, 0, 0, 27, 0, -22, 0, 0, 0, 6, 0, -5, 0, 0, 0, 12, 0, -10, 0, 0, 0, 100, 0, -3, 0, 0, 0, -15, 0, 29, 0, 0, 0, -70, 0, 36, 0, 0, 0, -39, 0, 15, 0, 0, 0, -8, 0, 64, 0, 0, 0, 20, 0, -19, 0, 0, 0, -27, 0, 5, 0, 0, 0, 32, 0, -17, 0, 0, 0, 9, 0, -53, 0, 0, 0, -10, 0, 20, 0, 0, 0, 3, 0, -25, 0, 0, 0, -90, 0, 44, 0, 0, 0, 19, 0, -20, 0, 0, 0, -2, 0, 0, 0, 0, 0, -18, 0, 17, 0, 0, 0, -72, 0, -30, 0, 0, 0, -36, 0, -50, 0, 0, 0, 21, 0, 35, 0, 0, 0, 39, 0, 24, 0, 0, 0, -13, 0, 4, 0, 0, 0, -9, 0, -47, 0, 0, 0, 72, 0, -11, 0, 0, 0, -65, 0, -12, 0, 0, 0, 48, 0, -50, 0, 0, 0, -23, 0, 2, 0, 0, 0, -21, 0, 68, 0, 0, 0, 39, 0, -1, 0, 0, 0, 17, 0, -13, 0, 0, 0, -6, 0, -54, 0, 0, 0, 36, 0, -23, 0, 0, 0, 28, 0, -40, 0, 0, 0, -3, 0, -32, 0, 0, 0, 5, 0, 26, 0, 0, 0, -10, 0, -5, 0, 0, 0, 10, 0, 1, 0, 0, 0, -32, 0, -36, 0, 0, 0, 5, 0, 11, 0, 0, 0, 0, 0, -24, 0, 0, 0, 7, 0, 11, 0, 0, 0, 15, 0, -12, 0, 0, 0, -33, 0, -14, 0, 0, 0, 37, 0, 42, 0, 0, 0, -44, 0, -11, 0, 0, 0, -55, 0, 6, 0, 0, 0, 6, 0, 96, 0, 0, 0, -35, 0, 48, 0, 0, 0, 3, 0, 42, 0, 0, 0, -21, 0, -6, 0, 0, 0, 28, 0, -15, 0, 0, 0, -26, 0, 41, 0, 0, 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, 7, 3, 1, 3, 0]], "char_orbit_index": 19, "prim_orbit_index": 3, "minimal_twist": "56.2.i.b", "char_is_minimal": true, "conrey_index": 289, "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], [1, 0], [0, 0], [0, 0], [0, 0], [-1, 1], [0, 0], [-3, 2], [0, 0], [0, 0], [0, 0], [0, 3], [0, 0], [-6, 0], [0, 0], [0, 0], [0, 0], [0, -5], [0, 0], [-1, 1], [0, 0], [0, 0], [0, 0], [-7, 7], [0, 0], [0, 4], [0, 0], [0, 0], [0, 0], [-2, 0], [0, 0], [0, 5], [0, 0], [0, 0], [0, 0], [1, -3], [0, 0], [-3, 3], [0, 0], [0, 0], [0, 0], [2, 0], [0, 0], [-4, 0], [0, 0], [0, 0], [0, 0], [5, -5], [0, 0], [5, -8], [0, 0], [0, 0], [0, 0], [0, -1], [0, 0], [-3, 0], [0, 0], [0, 0], [0, 0], [0, 15], [0, 0], [5, -5], [0, 0], [0, 0], [0, 0], [6, -6], [0, 0], [0, 9], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -7], [0, 0], [0, 0], [0, 0], [-6, -3], [0, 0], [-1, 1], [0, 0], [0, 0], [0, 0], [-12, 0], [0, 0], [5, 0], [0, 0], [0, 0], [0, 0], [7, -7], [0, 0], [18, -12], [0, 0], [0, 0], [0, 0], [0, -1], [0, 0], [-2, 0], [0, 0], [0, 0], [0, 0]]}