# Stored data for newform 546.2.i.e, downloaded from the LMFDB on 28 March 2024. {"label": "546.2.i.e", "space_label": "546.2.i", "level": 546, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014948298850850, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 630263309358240589, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [4, -2, 1]], [17, [25, 5, 1]]], "qexp_display": "q+\\zeta_{6}q^{2}+(-1+\\zeta_{6})q^{3}+(-1+\\zeta_{6})q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "i", "char_is_real": false, "Nk2": 2184, "analytic_conductor": 4.359831950361909, "hecke_ring_index": 1, "level_radical": 546, "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": "0.012", "prec": 17}, "analytic_rank_proved": true, "char_values": [546, 3, [365, 157, 379], [3, 1, 3]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 7, 13], "conrey_indexes": [79, 235], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.027", "prec": 17}, {"__RealLiteral__": 0, "data": "2.074", "prec": 17}, {"__RealLiteral__": 0, "data": "0.097", "prec": 17}, {"__RealLiteral__": 0, "data": "13.299", "prec": 20}, {"__RealLiteral__": 0, "data": "1.023", "prec": 17}, {"__RealLiteral__": 0, "data": "127.965", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [1, -1, 2, -5], "traces": [0, 2, 1, -1, -1, 2, -2, -5, -2, -1, -2, -3, -1, -2, -1, -4, -1, -5, 1, -1, -4, 4, -6, 0, 1, 1, -1, 2, 4, -2, -2, -4, 1, -3, -10, -2, 2, 2, 1, 1, -2, 20, 5, -20, -3, 2, 0, 1, 2, 11, 2, -5, 1, 3, 1, -12, 5, 2, -1, -3, 2, 5, -8, 1, 2, -2, 3, -5, -5, 0, 8, -2, 1, -12, -2, 1, 2, 12, 2, 6, 2, -1, 10, 32, 1, -20, -10, 1, 3, 14, 4, 5, 0, -4, -1, 2, 1, 8, -2, 6, 1, -2, 5, 2, 2, 10, 6, -12, -1, 16, -6, -4, 1, 30, 1, 0, 1, 1, -6, 20, 4, 2, -5, -10, -4, 24, -4, 0, 1, 10, 2, 4, 6, 1, -10, 2, 5, -18, 0, 4, 10, -2, -1, 3, -1, -2, -24, -13, -4, -8, -1, -19, 1, 10, 15, -16, 1, -21, -6, 3, 4, 0, -2, -19, -10, 6, 16, 42, -4, 2, -10, -1, 10, -3, 2, -4, 6, -3, -14, -2, 2, 6, 1, -10, 0, -4, 4, -15, -2, -5, 4, -20, -1, 14, 4, 4, -13, -48, 3, 20, -1, -5, -4, 5, 10, 20, -2, 0, 1, 6, 2, -32, 3, 1, 12, -20, -2, 16, 32, -12, 6, 5, -2, 22, -4, -2, 15, -8, -1, -6, 0, 3, 2, -11, -1, -2, -3, -12, 25, 42, 2, -4, -2, -1, -10, -4, -20, 1, 4, -16, 12, -36, -5, 0, 0, 10, -1, -6, 20, -2, 4, 1, -4, 6, 3, 12, -4, -28, -5, 9, -2, -11, 10, -4, -36, 3, 0, 27, 2, 8, 2, 32, -1, -4, 1, 2, 6, -50, -2, -8, 2, -4, -12, -24, -11, -12, -2, -3, 8, 0, -2, 50, -38, -2, -1, -10, 5, -54, 3, -4, -8, -14, -1, -34, -42, -8, -12, 6, -3, 3, 2, 24, 0, 10, -1, -1, 19, 16, -20, -1, 12, 20, -16, 2, 21, -20, -5, -34, 1, -15, 10, -12, -2, -20, 20, 0, 3, -2, 1, 72, -5, -2, 3, -14, 3, -2, -28, 5, -4, 0, -2, 18, 3, -4, -4, -48, -5, -26, 0, -10, -8, -12, 8, -13, 15, -12, -1, 2, -1, 56, 2, 0, 20, 32, -2, 30, 28, 10, -4, -9, 2, 0, -11, -8, -24, -12, -3, -36, 40, -5, -2, 36, 5, 4, -2, -4, 1, -12, 5, 30, -20, -18, -4, 12, 0, 32, -1, -2, 3, 20, -8, 16, -16, 1, -3, 5, 2, -5, 24, 3, 20, 8, -1, -38, 20, 4, 16, 0, 12, -40, 12, 2, 10, 18, 2, -28, 11, 16, -5, -16, -1, -30, -15, -19, -16, 2, -2, 16, 6, -5, 0, 40, -12, 16, 1, 8, 11, 24, -2, 20, -4, -21, 3, 30, -6, -2, 5, -6, 21, 33, -2, -2, -8, 0, -4, 8, 1, -11, -5, 38, -26, 44, -10, 5, -1, 6, 8, 5, -32, 28, -12, -21, -18, -24, -1, -8, 0, -1, 0, 28, 20, 48, -2, -1, 6, -4, 10, -6, 8, 6, 2, -42, -1, -6, -8, -1, 12, -20, -3, 23, 6, 6, -5, -20, -14, 24, 5, -2, 18, -39, -4, 34, 11, -3, 5, 64, -5, 56, -18, 5, -3, 1, 0, -6, 54, -4, -2, -18, 4, 20, -8, 30, 16, -24, 1, 30, -8, 4, 2, -19, -2, -36, 3, 40, -10, 0, -1, -38, 8, 14, 4, -80, -8, 9, 12, -2, -12, 62, 2, 8, -6, 24, 2, -14, -6, 50, 16, 20, 0, 38, -1, -38, 10, 10, -19, -4, 2, 12, -2, -4, -20, -1, -5, 16, -27, -40, -12, 68, -2, 4, 8, 0, -28, -14, -2, 19, 34, -3, -21, -20, -10, 96, -6, 16, -6, 0, -6, -11, 6, 1, -2, -30, 12, -38, 0, 40, 5, 38, 1, -9, -2, 4, 38, -18, -16, -8, -10, 24, 4, 12, 6, 26, -20, 5, -32, -8, 4, 0, -21, -11, -10, -30, -1, 28, -17, 1, -1, 3, -30, -20, 20, -8, 12, 12, -1, -72, 17, 12, 10, -3, 0, 17, 6, -15, -4, 4, -1, -50, 36, 22, -1, -100, -1, 2, -3, -2, -28, 8, 6, -20, 2, 6, -14, 0, -20, 12, -2, -21, 0, 18, -4, -2, 36, -4, -3, -1, -2, 24, -5, 2, -24, 50, 5, 40, -52, -22, 0, -15, 10, -40, -4, -2, -15, -6, 4, 16, 13, -16, 30, 12, -24, 12, 1, 18, 1, -76, 4, -74, 28, 0, -2, -12, 0, -64, 40, 10, -32, 3, -1, -88, 6, 12, 14, -26, -10, 4, -8, 10, -18, -10, -2, 3, 0, -2, 2, -84, -4, 5, 24, 6, -24, -75, -6, -5, 36, -6, 20, 4, -1, -10, -1, 14, -36, -36, 10, 0, 8, 9, 2, 5, -2, -56, -4, 22, -6, 38, -5, 10, 60, -1, -40, -42, 18, 30, -2, -6, 15, -70, 0, 19, -32, 27, -2, -65, -4, 42, -3, -4, 10, -18, -10, -56, 8, -16, 16, 2, 2, -2, -6, -4, -5, 0, 1, -80, 20, -4, 12, -3, -3, 40, 40, 40, 16, 44, 1, 6, -19, 16, 4, -36, 2, 5, -16, -4, 0, -60, 24, -22, 40, 12, 6, -52, 13, -76, 5, 6, -18, 14, 4, 0, -56, -3, -11, 1, 8, -8, -1, 0, -8, 4, 1, 15, -60, -40, -30, 6, 19, -28, -8, 4, -8, 52, -1, -48, -16, -10, 12, -4, -10, 2, 0, 27, 20, 2, -15, 4, 8, 2, -1, 46, 16, 2, 22, -14, -24, 30, -1, -10, 25, 68, -2, 24, 21, 0, 6, -2, 60, 25, 6, 12, -1, -12, -20, 38, -3, 40, -21, 3, 66, 72, -4, 15, 2, -12, -4, 56, 0, -62, -2, -5, -8, 14, 2, -10, -22, -1, 5, -62, 19, -84, -22, -32, 22, 59, 10, -48, 10, 5, -2, 0, -6, 48, 4, -40, 1, 80, -16, -19, -28, 2, -24], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "char_orbit_index": 9, "prim_orbit_index": 3, "minimal_twist": "546.2.i.e", "char_is_minimal": true, "conrey_index": 79, "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, 1], [-1, 1], [-1, 1], [0, 2], [-1, 0], [-2, -1], [-1, 0], [0, -1], [-2, 2], [-3, 3], [0, -1], [-1, 0], [1, -3], [-2, 0], [0, -1], [-5, 5], [1, -1], [0, -1], [-2, 0], [3, -2], [-3, 0], [0, 0], [1, -1], [1, -1], [0, -1], [1, 0], [3, -2], [-1, 0], [0, -2], [-4, 4], [1, -1], [0, -3], [-5, 0], [2, -6], [1, 0], [0, 2], [1, -1], [1, -1], [0, -2], [10, 0], [2, 1], [-10, 0], [0, -3], [2, -2], [0, 0], [0, 1], [1, 0], [3, 5], [1, 0], [0, -5], [1, -1], [3, -3], [0, 1], [-6, 0], [2, 1], [1, 0], [0, -1], [-3, 3], [2, -2], [0, 5], [-4, 0], [-1, 3], [1, 0], [0, -2], [3, -3], [-5, 5], [0, -5], [0, 0], [6, -4], [-1, 0], [0, 1], [-12, 12], [-2, 2], [0, 1], [1, 0], [9, -6], [1, 0], [0, 6], [2, -2], [-1, 1], [0, 10], [16, 0], [-1, 3], [-10, 0], [0, -10], [1, -1], [3, -3], [0, 14], [2, 0], [2, 1], [0, 0], [0, -4], [-1, 1], [2, -2], [0, 1], [4, 0], [-5, 8], [3, 0], [0, 1]]}