# Stored data for newform 504.2.cj.c, downloaded from the LMFDB on 26 April 2024.
{"label": "504.2.cj.c", "space_label": "504.2.cj", "level": 504, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9011391176376824, "dim": 12, "is_polredabs": true, "nf_label": "12.0.951588245534976.1", "trace_hash": 1522907606681954531, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [49, 0, -189, 0, 638, 0, -337, 0, 142, 0, -13, 0, 1]]], "qexp_display": "q+(\\beta _{1}-\\beta _{5})q^{2}-\\beta _{3}q^{4}+(-\\beta _{1}+\\beta _{5}+\\cdots)q^{5}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 56, "char_orbit_label": "cj", "char_is_real": false, "Nk2": 2016, "analytic_conductor": 4.024460261872531, "hecke_ring_index": 4, "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": "0.506", "prec": 17}, "analytic_rank_proved": true, "char_values": [504, 6, [127, 253, 281, 73], [6, 3, 6, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [2, 3, 7], "conrey_indexes": [37, 109], "field_disc": 951588245534976, "field_disc_factorization": [[2, 8], [3, 6], [7, 2], [101, 4]], "field_poly": [64, -32, 32, -72, 32, -26, 35, -13, 8, -9, 2, -1, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.067", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "940.044", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "130500.350", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.3.c6", "trace_display": [2, 0, 0, -4], "traces": [0, 12, 2, 0, 0, 0, 0, -4, -4, 0, -8, 0, 0, 0, 16, 0, 8, 2, 0, 0, -8, 0, 12, -2, 0, -4, 2, 0, 26, 0, 0, 10, 12, 0, 32, 0, 0, 0, -18, 0, 10, 8, 0, 0, 30, 0, -4, -30, 0, -12, 16, 0, -32, 0, 0, 4, 40, 0, -22, 0, 0, 0, 28, 0, 24, -8, 0, 0, -4, 0, -48, -32, 0, -10, -18, 0, 52, 0, 0, -22, -36, 0, -26, 0, 0, 0, -40, 0, -14, 10, 0, 0, 20, 0, 42, 34, 0, 40, -52, 0, -20, 0, 0, -46, 8, 0, -44, 0, 0, 0, 8, 0, -36, -24, 0, 0, -28, 0, -72, 46, 0, 8, 50, 0, 6, 0, 0, -112, -40, 0, 6, 0, 0, 0, -40, 0, 38, -14, 0, 0, -40, 0, 28, -60, 0, 24, -12, 0, -64, 0, 0, 26, -2, 0, 46, 0, 0, 0, 24, 0, -88, -10, 0, 0, 28, 0, 16, -40, 0, 28, 26, 0, 12, 0, 0, 100, -32, 0, -22, 0, 0, 0, 22, 0, 30, 14, 0, 0, 36, 0, 32, 10, 0, -42, -30, 0, 48, 0, 0, -54, 60, 0, 72, 0, 0, 0, -20, 0, 12, 100, 0, 0, 36, 0, 2, 84, 0, -6, 0, 0, -42, 0, 0, 16, 48, 0, 2, 0, 0, 0, -44, 0, 40, 10, 0, 0, -14, 0, -26, 120, 0, 38, -42, 0, 64, 0, 0, 52, 6, 0, 4, 0, 0, 0, -28, 0, 32, 18, 0, 0, -72, 0, 36, -70, 0, -44, -24, 0, -6, 0, 0, 90, -56, 0, -64, 0, 0, 0, 28, 0, 30, 24, 0, 0, -44, 0, -52, -56, 0, 32, -2, 0, -52, 0, 0, 188, -22, 0, -12, 0, 0, 0, 124, 0, -32, -26, 0, 0, 12, 0, 12, 106, 0, -2, 100, 0, 44, 0, 0, -36, 12, 0, -26, 0, 0, 0, 32, 0, 0, -90, 0, 0, -8, 0, 14, 84, 0, 40, 26, 0, -44, 0, 0, -148, -8, 0, 14, 0, 0, 0, -28, 0, -64, 34, 0, 0, 80, 0, 4, -22, 0, 8, -12, 0, 8, 0, 0, 30, 12, 0, -8, 0, 0, 0, 52, 0, -18, -112, 0, 0, -10, 0, -2, -102, 0, -56, -16, 0, 8, 0, 0, 76, -52, 0, 46, 0, 0, 0, -204, 0, -48, 58, 0, 0, -60, 0, 74, -172, 0, 30, -34, 0, 36, 0, 0, -52, 48, 0, 4, 0, 0, 0, 40, 0, 66, -76, 0, 0, -36, 0, -44, 54, 0, -248, 2, 0, 24, 0, 0, -122, -140, 0, 140, 0, 0, 0, 48, 0, 8, 88, 0, 0, -16, 0, 12, 68, 0, -42, -80, 0, -38, 0, 0, -208, -4, 0, -76, 0, 0, 0, 72, 0, -22, 20, 0, 0, 34, 0, -14, -142, 0, -64, 196, 0, -120, 0, 0, 46, 74, 0, -86, 0, 0, 0, 38, 0, -16, 56, 0, 0, -56, 0, 38, -80, 0, -44, 22, 0, -20, 0, 0, 206, 176, 0, 88, 0, 0, 0, -42, 0, -76, 26, 0, 0, 260, 0, 24, -34, 0, 108, -44, 0, -160, 0, 0, -74, -2, 0, -44, 0, 0, 0, 32, 0, -12, -276, 0, 0, -28, 0, 44, 124, 0, -70, -68, 0, 64, 0, 0, 48, -84, 0, 114, 0, 0, 0, -244, 0, -32, -22, 0, 0, -16, 0, -46, 120, 0, 22, -44, 0, 32, 0, 0, 6, 102, 0, -24, 0, 0, 0, 58, 0, 8, -54, 0, 0, -136, 0, -38, -38, 0, 88, 112, 0, 30, 0, 0, 126, -240, 0, 48, 0, 0, 0, 108, 0, 114, -104, 0, 0, -10, 0, -72, -46, 0, 10, -58, 0, 32, 0, 0, 160, 18, 0, -82, 0, 0, 0, 68, 0, -48, 130, 0, 0, 28, 0, -36, 122, 0, -6, 152, 0, 164, 0, 0, -54, 60, 0, -96, 0, 0, 0, 64, 0, 40, 38, 0, 0, -100, 0, 22, 276, 0, -40, 46, 0, -12, 0, 0, -144, 68, 0, 36, 0, 0, 0, -62, 0, -88, -72, 0, 0, 232, 0, -16, 4, 0, -52, -78, 0, -16, 0, 0, -14, 52, 0, -16, 0, 0, 0, 76, 0, 114, 12, 0, 0, -34, 0, 98, -138, 0, 50, -172, 0, 76, 0, 0, 64, -56, 0, 88, 0, 0, 0, -232, 0, 32, -10, 0, 0, -68, 0, 138, -32, 0, 42, -22, 0, 12, 0, 0, -130, -24, 0, 64, 0, 0, 0, 18, 0, 18, 122, 0, 0, 52, 0, -10, 28, 0, 232, 124, 0, 16, 0, 0, -12, -128, 0, -56, 0, 0, 0, -10, 0, 68, -52, 0, 0, -92, 0, 4, 0, 0, 64, -100, 0, -22, 0, 0, -204, -32, 0, 44, 0, 0, 0, 68, 0, -50, -30, 0, 0, 100, 0, -94, -130, 0, 140, 184, 0, -64, 0, 0, 38, 122, 0, -50, 0, 0, 0, 36, 0, 0, 26, 0, 0, -56, 0, 4, -192, 0, 60, -14, 0, -128, 0, 0, 196, 176, 0, -20, 0, 0, 0, 34, 0, -70, 58, 0, 0, 184, 0, 68, -82, 0, -142, -42, 0, 64, 0, 0, 12, 138, 0, 20, 0, 0, 0, 134, 0, -12, 360, 0, 0, -20, 0, 22, 90, 0, -40, -224, 0, -76, 0, 0, 36, -8, 0, -26, 0, 0, 0, -100, 0, -32, 88, 0, 0, -86, 0, 102, -32, 0, 4, -14, 0, 0, 0, 0, 6, -6, 0, -102, 0, 0, 0, -96, 0, 104, 146, 0, 0, -208, 0, -52, -54, 0, -312, -14, 0, 30, 0, 0, 0, -232, 0, 88, 0, 0, 0, -20, 0, 94, 8, 0, 0, -44, 0, -176, 62, 0, 148, 58, 0, 48, 0, 0, 80, -44, 0, -6, 0, 0, 0, -136, 0, -48, -214, 0, 0, 28, 0, -106, 118, 0, -16, 108, 0, -64, 0, 0, 70, -8, 0, 56, 0, 0, 0, 80, 0, -76], "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], [1, 1, 8, 2, 1, 2, 0], [1, 1, 56, 16, 1, 6, 0]], "char_orbit_index": 62, "prim_orbit_index": 16, "minimal_twist": "56.2.p.a", "char_is_minimal": true, "conrey_index": 37, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, -1, 0, 0, 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, -1, 0, 0, 0, 1, 1, -1, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, -1, 1, 0, 0, 0, -1, -1, 1, 0, 0], [-1, 1, -1, 0, 0, 0, 0, -1, -1, 1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, -1, 0, 1, 0, 1, 0, 1, 0], [0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0], [2, -1, 0, 0, -1, 0, -1, 0, -1, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, -2, 0, -2, 2, 0, 0, 0, 2], [0, 0, 0, -1, -1, 2, 0, 0, -2, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, -1, -1, 0, 2, 1, -2, 0, -1, 0, -1], [0, -2, 2, 0, 0, 0, 0, 0, 0, -1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, -2, -2, 1, 0, 2], [-1, 1, -1, 1, 1, -1, 0, -1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, -2, 2, 0, 0, -2, 0, -2, 0], [-1, 1, -1, 1, 1, -1, -1, -3, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, -1, -1, 1, -2, -3, 0, -1, -2], [0, 2, 1, 0, 0, 0, 0, 2, 2, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 2, -2, -2, 0, -2, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, -1, 0, 0, 0, 0, 1, 1, -1, -1, 1], [0, 0, 0, 1, 0, 2, 1, 0, 2, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 1, 1, 0, 1, -1, -1, 0, 1, 0, 1], [0, 0, 0, 1, -4, 1, 2, 0, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 1, 1, -1, 1, 1, -3, 0, 1, 0, -1], [2, -2, -1, 0, 0, 0, 0, 2, 2, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 4, 4, 0, 0, 2], [5, 1, 1, 0, -5, -1, -3, 1, 0, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, -1, 0, -1, 0, 1, 0], [-3, -3, 0, 0, 3, 3, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, -1, 2, 0, -2, 0, 2, 4, 1, 1, 0], [2, 0, -2, 0, 0, 0, 0, 2, 2, 0, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -6, 0, -2, 0, -2, 0, 0, 0], [0, 0, 0, -1, 0, 1, -3, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 3, 0, 0, 0, 0, 1, 1, -3, 3, 0], [5, 1, -1, 0, -2, -2, 2, 1, 3, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 1, -1, -1, 5, -1, -1, -3, 0, -1, 0, 1], [0, 0, 0, 0, 0, 4, 3, 0, 4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, -1, -1, 0, -3, 3, 3, 0, -1, 0, -3], [2, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, -2, 0, 0, 0, 0, 2, 2, 2, -2, -2], [0, -2, 3, -3, 0, 2, 0, 2, 0, -3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 1, 0, 2, 0, 0, 0], [0, 2, 2, -1, 0, -2, 0, 4, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -1, 1, 0, 1, 0, 1, 3, 4, -3, 2, -1], [-4, 2, 2, 0, 0, 0, 0, -2, -2, -2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -4, -3, 2, 0, 0, -2, 0, -4, 0], [0, 0, 0, 2, -2, -1, -2, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [7, -5, 3, 0, 0, 0, 0, 3, 3, -2, 3, 1], [0, -2, -1, 0, 0, -1, 3, -2, -3, -1, -1, -6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -1, -1, 1, 3, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 2, -4, -2, 0, 0, 4, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 3, -1, 3, 5, -3, -1, 1, 0, 3, 0, 1], [0, -2, 0, 0, 0, 0, 0, -2, -2, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 1, 0, 0, 0, 0, -3, -3, 1, 1, -3], [-6, 0, 2, -4, 6, 0, -2, 2, 0, -4, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, -1, -5, -3, 0, -1, 0, -3, 0], [-1, 4, -4, 4, 1, -4, 0, -4, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -4, -1, 0, 0, 2, 4, -4, -2, -1, -1, -2], [1, -1, -1, 0, 0, 0, 0, -3, -3, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 6, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 5, 1, 0, 0, -1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, -4, 1, 0, 0, 0, 0, 4, 4, -1, 1, 0], [-7, 0, 1, 3, 5, -2, -1, -1, -2, 3, 2, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 2, 2, 0, 2, -2, -2, 6, 0, 0, 0, 2]]}