# Stored data for newform 726.2.e.k, downloaded from the LMFDB on 20 April 2024.
{"label": "726.2.e.k", "space_label": "726.2.e", "level": 726, "weight": 2, "hecke_orbit": 11, "hecke_orbit_code": 45036271185167062, "dim": 4, "is_polredabs": true, "nf_label": "4.0.125.1", "trace_hash": 418323567198264700, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [0, 1]], [7, [16, 8, 4, 2, 1]], [13, [256, -64, 16, -4, 1]]], "qexp_display": "q+(1-\\zeta_{10}+\\zeta_{10}^{2}-\\zeta_{10}^{3})q^{2}+\\zeta_{10}^{2}q^{3}+\\cdots", "char_order": 5, "char_parity": 1, "char_degree": 4, "char_conductor": 11, "char_orbit_label": "e", "char_is_real": false, "Nk2": 2904, "analytic_conductor": 5.797139186744956, "hecke_ring_index": 1, "level_radical": 66, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 10, "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": "0.019", "prec": 17}, "analytic_rank_proved": true, "char_values": [726, 5, [485, 607], [5, 4]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 4, "level_primes": [2, 3, 11], "conrey_indexes": [487, 493, 511, 565], "field_disc": 125, "field_disc_factorization": [[5, 3]], "field_poly": [1, -1, 1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.038", "prec": 17}, {"__RealLiteral__": 0, "data": "3.896", "prec": 17}, {"__RealLiteral__": 0, "data": "2.854", "prec": 17}, {"__RealLiteral__": 0, "data": "98.994", "prec": 20}, {"__RealLiteral__": 0, "data": "148.917", "prec": 24}, {"__RealLiteral__": 0, "data": "3907.605", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c5", "trace_display": [1, -1, 0, -2], "traces": [0, 4, 1, -1, -1, 0, 1, -2, 1, -1, 0, 0, 4, 4, 2, 0, -1, 6, 1, 4, 0, 8, 0, 24, 1, 5, -4, -1, -2, -6, 0, -8, -4, 0, 24, 0, -1, 10, -4, 4, 0, -6, 2, 32, 0, 0, 6, 6, -1, 3, -5, 6, 4, 0, -4, 0, -8, 4, 6, 0, 0, -8, 8, -2, -1, 0, 0, -16, 6, -6, 0, -6, 1, -2, -10, 5, -16, 0, 16, -14, 0, -1, 6, 12, -2, 0, 8, 24, 0, -24, 0, 8, -6, -8, -6, 0, 1, -14, 12, 0, -20, -6, -6, 4, -4, 0, 0, 12, -1, -16, 0, -40, -2, -18, -4, 0, -6, 4, 0, 12, 0, 0, -32, -6, -8, 0, 2, -14, 1, -8, 0, -48, 0, -32, -4, 0, -6, 18, 6, 4, 0, 6, -24, 0, 4, 0, 2, 3, 10, 6, -5, 10, -4, -24, 0, 0, 4, -2, 14, 0, 0, -12, 1, 4, 24, 0, 48, -12, 2, -3, 0, 4, -8, -6, 6, -40, 0, 0, -6, -24, 0, 22, -8, -8, 6, 0, -32, 0, -24, -2, 0, -18, -1, -14, 14, 0, 3, 24, 0, -16, -5, 4, 6, -12, 6, 0, -4, -6, -16, 0, 0, -8, 0, -6, -12, 0, 1, -16, -4, 8, 0, 96, -10, 16, 2, 5, 18, 12, 4, 22, 0, 0, -24, 18, -4, 0, 0, -14, -12, 12, 0, -40, 0, 4, -8, 0, 6, -16, 8, 12, 0, 0, 8, 0, -56, 0, -1, 30, 8, 20, 0, -6, -12, 0, 0, 0, -8, 6, 4, 24, 0, -2, 6, 8, 72, 0, 24, 16, -4, -8, 0, 6, -6, -8, -6, 0, 0, 48, 1, -19, 0, -14, -2, 6, -3, 0, 40, 0, 24, 24, 5, -16, -10, -6, 4, 0, -6, 80, 0, -16, 0, 18, -4, -26, 2, 0, -14, -12, 0, 0, 0, 12, 12, -24, -1, -20, -4, 4, 6, -48, 0, -16, 12, 10, 12, 0, -2, -2, 3, -18, 0, 0, 16, 20, 8, 0, 6, -36, -6, 4, -10, -16, 0, -24, 0, 0, 6, 12, 24, 12, 0, 3, 88, 0, -32, 0, 8, -8, -6, -6, 0, 0, -8, 80, 0, 0, -6, 24, 2, -20, 0, -14, 18, -6, -4, 0, -56, -8, -14, 0, 0, 36, -3, 12, 6, 0, 0, 104, -4, 8, 5, -30, -4, 32, -6, 0, -48, 0, 24, 34, 0, 18, 4, 0, 6, 0, -4, -16, 0, 96, 0, 10, 8, 6, 0, -30, 6, -16, -48, 0, 0, 0, -1, -26, 16, 0, 4, 24, 2, -40, 0, -12, 24, 24, 10, 0, -16, 6, -2, -6, 20, 0, 72, 10, -12, 0, -4, 10, -22, 6, 0, 168, 0, -16, -6, 0, -18, 12, 4, 8, 0, -2, 0, 0, -56, -20, 12, 0, -12, 24, 0, -40, -10, 48, 0, 0, 1, -20, 8, 4, 0, -12, -6, 36, -64, 0, 32, -12, -12, 4, 0, -12, 0, -12, 2, 0, 0, 12, -14, -24, 0, -4, 1, 4, -30, 0, 32, 0, 80, -6, 0, 18, 6, 16, 12, 10, 0, -192, 0, 52, 0, 0, 8, 24, -6, 0, -4, -24, 96, 0, 0, -20, 2, 22, -6, 0, -8, 28, 18, 32, 0, -96, 6, -28, -16, 0, 4, -18, 8, 32, 0, 0, 24, 12, 6, 0, 8, -2, 6, -18, 0, -112, 0, 72, 12, 30, -1, 34, 19, -14, 0, 24, -56, 0, -8, 0, -6, -24, 3, 32, 0, -6, 10, -120, 0, 0, 6, 4, -24, -30, -5, 22, 16, 4, -40, 0, -24, -14, -4, -12, 0, -24, 6, 16, 20, 0, 0, -120, -4, -44, 0, -6, -18, 12, 4, -25, -104, 0, 8, -60, 0, 16, 14, -8, 12, 0, 0, 48, 0, 24, 0, -6, -12, 4, -12, 0, 24, -6, -4, 0, -80, -16, 4, 36, -4, 0, -6, -2, -12, 144, 0, -88, -4, -24, -12, 0, -10, -36, -12, 16, 0, 0, -8, -14, 2, 5, -3, -30, 18, -28, 0, -48, 0, -96, 4, 0, -20, 22, -8, 0, 0, -20, 24, 0, -144, 0, 6, 36, -4, 18, 10, 6, -4, 160, 0, 0, -6, -12, 0, -26, 0, -14, -6, -48, 48, 0, 96, 12, -12, -30, 0, 8, -3, 10, 22, -120, 0, -112, -8, -1, 0, 48, -8, 4, 8, 0, -24, 0, -24, -8, 0, -16, 0, -36, 8, 0, 20, -48, 0, -96, 0, -8, 6, 0, -24, 0, -2, 34, -80, 0, 0, -18, 14, 8, -18, 0, 6, 0, -1, -136, 0, -120, -14, 0, 8, 40, 14, 20, 0, 24, 0, 0, 144, -6, 3, 0, -12, -32, -6, 0, 0, 144, 0, -128, 26, 0, 4, 0, -8, -36, -5, 6, -120, 0, -16, 0, -32, 24, 6, 42, 0, -8, -12, 8, 0, 0, 6, 32, -34, 8, 0, 18, -18, -8, 16, 0, 0, 12, -6, -14, 0, 16, 4, -18, -4, 0, 0, 32, 24, -18, 0, -7, -10, 6, -8, 0, 24, 0, 0, -8, 30, 60, -6, -8, 16, 0, -12, 216, 0, 80, 0, -12, 0, -42, 1, 0, 26, -19, 64, 0, 0, -16, -4, -14, -24, 0, -2, 52, -10, -24, 0, -120, -3, 28, -24, 0, -24, 36, -10, -28, 0, 0, -64, -24, -6, 0, 2, 24, 6, -48, 5, 0, 0, 64, 18, 0, -10, -20, 12, -6, 0, 42, -16, 0, 40, 0, 22, 24, -6, -2, 0, -20, 42, -96, 0, 200, -4, 4, 6, -30, 0, -12, 18, 18, 48, 0, 16, 22, -8, -26, 0, 18, 2, -36, 0, 0, 0, 48, -14, 8, 20, -12, -12, 42, 0, 0, -48, 0, 96, 36, 0, -33, 40, 12, 10, 0, 12, 56, 0, 96, 0, 0, -1, 8, 20, -20, -8, -54, 16, 0, 0, 4, 12, -30, 6, 0, -36, 12, -16, 192, 0, 224, 8, 4, 12, 0, 12, -44, -4, 10, 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, 3, 11, 3, 1, 5, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "66.2.a.a", "char_is_minimal": false, "conrey_index": 487, "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], [1, 0, 0, 0], [1, -1, 1, -1], [0, 0, 1, 0], [0, 0, 0, -1], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, -2], [0, 0, -1, 0], [-1, 1, -1, 1], [0, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [4, -4, 4, -4], [0, 0, -2, 0], [0, 0, 0, 0], [0, -1, 0, 0], [0, 6, 0, 0], [0, 0, 0, 1], [0, 0, -4, 0], [0, 0, 0, 0], [2, 0, 0, 0], [0, 0, 0, 0], [6, 0, 0, 0], [1, -1, 1, -1], [0, 0, -5, 0], [0, 0, 0, -4], [0, -1, 0, 0], [0, -2, 0, 0], [0, 0, 0, -6], [0, 0, 0, 0], [-8, 8, -8, 8], [-1, 0, 0, 0], [0, 0, 0, 0], [6, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 10], [0, -4, 0, 0], [0, 4, 0, 0], [0, 0, 0, 0], [0, 0, 6, 0], [2, -2, 2, -2], [8, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [6, -6, 6, -6], [0, 0, -6, 0], [0, 0, 0, -1], [0, 3, 0, 0], [0, -5, 0, 0], [0, 0, 0, 6], [0, 0, -4, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [-2, 0, 0, 0], [4, -4, 4, -4], [0, 0, -6, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -8, 0, 0], [0, 0, 0, 8], [0, 0, 2, 0], [-1, 1, -1, 1], [0, 0, 0, 0], [0, 0, 0, 0], [-4, 0, 0, 0], [6, -6, 6, -6], [0, 0, 6, 0], [0, 0, 0, 0], [0, -6, 0, 0], [0, 1, 0, 0], [0, 0, 0, -2], [0, 0, 10, 0], [5, -5, 5, -5], [-4, 0, 0, 0], [0, 0, 0, 0], [4, 0, 0, 0], [-14, 14, -14, 14], [0, 0, 0, 0], [0, 0, 0, -1], [0, 6, 0, 0], [0, 12, 0, 0], [0, 0, 0, -2], [0, 0, 0, 0], [8, -8, 8, -8], [6, 0, 0, 0], [0, 0, 0, 0], [-6, 0, 0, 0], [0, 0, 0, 0], [0, 0, -8, 0], [0, 0, 0, -6], [0, -8, 0, 0], [0, -6, 0, 0], [0, 0, 0, 0], [0, 0, -1, 0], [-14, 14, -14, 14], [3, 0, 0, 0], [0, 0, 0, 0], [-5, 0, 0, 0]]}