# Stored data for newform 539.2.e.a, downloaded from the LMFDB on 19 April 2024. {"label": "539.2.e.a", "space_label": "539.2.e", "level": 539, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 274911461915, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 920663648923528615, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [1, 1, 1]], [3, [4, 2, 1]]], "qexp_display": "q-\\zeta_{6}q^{2}+(-2+2\\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": "e", "char_is_real": false, "Nk2": 2156, "analytic_conductor": 4.303936668947013, "hecke_ring_index": 1, "level_radical": 77, "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": "0.023", "prec": 17}, "analytic_rank_proved": true, "char_values": [539, 3, [199, 442], [2, 3]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [7, 11], "conrey_indexes": [67, 177], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.956", "prec": 17}, {"__RealLiteral__": 0, "data": "0.063", "prec": 17}, {"__RealLiteral__": 0, "data": "11.663", "prec": 20}, {"__RealLiteral__": 0, "data": "0.220", "prec": 17}, {"__RealLiteral__": 0, "data": "105.494", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [-1, -2, 2, 0], "traces": [0, 2, -1, -2, 1, 2, 4, 0, -6, -1, 2, -1, 2, 8, 0, -8, 1, -4, -1, 0, 4, 0, 2, 4, 6, 1, -4, -8, 0, -12, 4, -10, -5, -2, 8, 0, -2, 6, 0, -8, -6, 8, 0, 24, 1, 2, 4, 10, -4, 0, -2, -8, 4, 6, 4, -4, 0, 0, 6, -2, -4, 0, 20, 0, 14, 8, -2, -8, 4, -16, 0, -24, 3, 8, 6, 2, 0, 0, 16, -8, -2, 11, -4, 0, 0, -16, -12, 12, 3, 6, -4, 0, 8, -20, 10, 0, -10, -20, 0, 2, -1, 4, -8, -14, -24, 0, -12, -12, -4, 14, 2, -24, 0, 36, 0, -8, -6, -4, 4, 0, 24, -1, 0, -8, 10, 24, 0, 16, 3, -24, 8, -12, -4, 0, 16, -8, 12, 10, 8, -16, 0, -40, 12, -4, 1, -12, -16, 0, 12, 10, 2, 16, 0, 8, 0, -40, 8, -14, -8, 12, -20, 0, -22, 8, 4, 4, 0, 0, 0, 6, 8, 0, 12, -12, -24, 0, -2, -4, 6, -12, -2, 20, 0, 0, -12, -12, -20, -4, 20, 0, 0, -8, -14, 14, 10, -32, 0, 44, -1, 18, -3, -16, -8, 0, -16, 8, -14, 4, 4, 0, 0, -24, -6, 24, -12, 24, 24, 0, -28, 16, -2, -16, 12, 44, 0, -2, -18, -12, 0, -18, 16, 0, 36, 18, -4, -20, 2, 32, 0, 0, -4, 20, -1, 10, 0, 0, 16, 0, 30, 0, -12, -4, 0, -8, -8, 16, 17, 14, 48, 0, 16, 6, -12, -8, 6, 24, 0, -24, 8, -10, -8, 4, -8, 0, -20, 1, -8, -22, 8, 20, 0, 12, 20, -4, -12, 0, 8, 0, 10, 1, -12, 20, -8, -48, 0, -8, -18, 4, 10, 16, 4, 0, -32, 8, 0, 0, -4, 40, 0, 56, 20, 18, 24, -2, 28, 0, -16, 2, 12, 6, 14, 48, 0, 0, -11, 4, 8, 28, -24, 0, -8, 20, 0, 6, 0, -32, 0, 28, -3, -36, -8, -10, 0, 0, -72, -16, -12, -4, -12, 0, 0, -32, -5, 30, -4, -24, 12, 0, 24, -16, -6, 19, -10, 4, 0, 32, 0, -22, -4, -4, 24, 0, -40, 26, -4, -24, -30, -48, 0, -16, 0, -16, -8, -2, -12, 0, -28, -12, -10, -6, 16, -32, 0, 48, -22, 16, 1, -22, -36, 0, 2, 22, -16, -40, -4, 44, 0, -12, 24, -24, 8, 20, -28, 0, -8, 0, -20, 16, 0, 4, 0, -28, 12, 10, -18, 4, -48, 0, -24, -8, 24, 0, -4, -52, 0, 48, -14, 0, 16, 20, 12, 0, 32, -4, -12, -12, -22, -40, 0, -20, 1, -4, 18, 32, 24, 0, 0, -18, -18, 16, 8, 0, 0, 8, -6, 40, 18, -30, -8, 0, 40, -28, 6, -12, -16, 0, 0, -12, 0, 4, 20, 24, -40, 0, -2, -20, 10, 28, 0, -32, 0, 56, 8, 24, 0, 2, -20, 0, 0, 16, 12, 0, 2, 8, 0, 16, 4, -6, 8, -18, -32, 0, -22, 0, 14, 28, 24, -20, 0, 48, -24, -6, 6, -20, -24, 0, 16, -40, 2, 7, -12, 4, 0, 32, 12, 24, 24, -24, 20, 0, -16, 26, 4, -20, -20, 56, 0, -56, -10, 0, 1, 0, 48, 0, 44, -24, -8, -22, -10, 96, 0, 16, -6, 32, -20, 36, 8, 0, 72, -30, 0, -20, 4, 32, 0, 8, -7, 18, 1, 28, -24, 0, -40, 6, -24, 8, 24, -4, 0, 0, 4, -44, -6, -32, -8, 0, 20, 36, 16, 20, -6, -56, 0, 16, -16, 2, 8, 40, 0, 0, 0, 40, 4, -26, -20, -32, 0, 12, -28, -14, -20, -16, -36, 0, -16, 19, -2, 0, 14, -48, 0, -16, 24, 24, 2, 16, 24, 0, -12, 12, -6, 18, -24, 28, 0, -96, 0, 22, -33, -2, -8, 0, 16, 26, 28, 24, 4, -16, 0, 8, -4, -22, 20, -32, 0, 0, -12, -24, 0, -44, 16, 0, 0, -68, -14, -4, 3, 12, 72, 0, 48, -24, -10, 4, 0, 40, 0, 72, 12, 24, -16, 46, -24, 0, 8, -16, -36, -16, 0, -72, 0, -44, 16, 0, -7, -40, -60, 0, -8, 34, -24, -8, -18, -80, 0, -16, 12, 0, -16, 6, 4, 0, -38, 40, 10, -6, -2, 36, 0, 26, -16, -48, 0, 0, 44, 0, -40, -8, -4, 4, 12, 0, 0, -16, 60, -20, 26, 0, -8, 0, 48, 20, -10, 4, 24, 64, 0, -20, 8, 8, 0, -48, 32, 0, -16, 8, -2, -8, 34, 64, 0, -56, -14, 30, -12, 10, 60, 0, 12, 0, -16, 12, 16, 48, 0, -56, -24, -16, 22, -16, -32, 0, -6, 0, -22, -24, -18, 28, 0, -80, 5, 6, 22, 8, -32, 0, 80, -20, -12, 30, -22, 56, 0, -16, 6, -16, 8, 0, 48, 0, 16, -46, 20, -24, 42, -4, 0, -56, -4, 2, 0, -44, 56, 0, -32, 0, 0, 40, -2, 68, 0, 14, 14, -12, -12, 6, -20, 0, 12, -8, 4, -24, -24, 88, 0, 0, 36, -56, -8, -6, 48, 0, 0, -24, 20, 24, 26, -4, 0, 16, -24, -32, -42, 10, 0, 0, 32, -42, 20, 48, -2, -68, 0, 56, 16, 8, -4, 28, 72, 0, 24, 11, 22, 0, 20, -48, 0, -64, 10, 60, -1, 24, 8, 0, -108, 20, 32, 0, 12, -8, 0, 72, 0, 0, -18, 0, -36, 0, -32, -40, 24, -40, 0, -96, 0, 12, -4, -14, 30, -6, -80, 0, 36, 36, -30, 8, 12, -32, 0, 8, 20, 24, -28, 16, -4, 0, 24, 36, 16, 32, 0, -8, 0, 68, 6, 16, 0, 12, -8, 0, -56, -69, 24, -12, -20, 56, 0, 80, 3, 0, -20, -14, 20, 0, -56, 8, 0, -42, 16, -12, 0, -28, -28, -54, 24, 44, -48, 0, 0, 48, 2, -52, -50, -80, 0, 72, 0, -20, 16, -24, -72], "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": 5, "prim_orbit_index": 3, "minimal_twist": "77.2.a.c", "char_is_minimal": false, "conrey_index": 67, "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], [-2, 2], [1, -1], [0, 2], [2, 0], [0, 0], [-3, 0], [0, -1], [2, -2], [-1, 1], [0, 2], [4, 0], [0, 0], [-4, 0], [0, 1], [-4, 4], [-1, 1], [0, 0], [2, 0], [0, 0], [1, 0], [0, 4], [6, -6], [1, -1], [0, -4], [-4, 0], [0, 0], [-6, 0], [0, 4], [-10, 10], [-5, 5], [0, -2], [4, 0], [0, 0], [-1, 0], [0, 6], [0, 0], [-8, 8], [0, -6], [4, 0], [0, 0], [12, 0], [0, 1], [2, -2], [4, -4], [0, 10], [-2, 0], [0, 0], [-1, 0], [0, -8], [4, -4], [6, -6], [0, 4], [-2, 0], [0, 0], [0, 0], [0, 6], [-2, 2], [-4, 4], [0, 0], [10, 0], [0, 0], [7, 0], [0, 8], [-2, 2], [-8, 8], [0, 4], [-8, 0], [0, 0], [-12, 0], [0, 3], [8, -8], [6, -6], [0, 2], [0, 0], [0, 0], [8, 0], [0, -8], [-2, 2], [11, -11], [0, -4], [0, 0], [0, 0], [-8, 0], [0, -12], [12, -12], [3, -3], [0, 6], [-2, 0], [0, 0], [4, 0], [0, -20], [10, -10], [0, 0], [0, -10], [-10, 0], [0, 0], [1, 0], [0, -1]]}