# Stored data for newform 539.4.a.g, downloaded from the LMFDB on 28 March 2024. {"label": "539.4.a.g", "space_label": "539.4.a", "level": 539, "weight": 4, "hecke_orbit": 7, "hecke_orbit_code": 27021597831332379, "dim": 4, "is_polredabs": true, "nf_label": "4.4.522072.1", "trace_hash": 1753817930413887436, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [112, -40, -27, 2, 1]], [3, [-1016, -436, 6, 14, 1]]], "qexp_display": "q+\\beta _{2}q^{2}+(-4-\\beta _{1})q^{3}+(6-\\beta _{2}-2\\beta _{3})q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 8624, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 31.802029493094192, "hecke_ring_index": 2, "level_radical": 77, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [539, 1, [199, 442], [1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [7, 11], "conrey_indexes": [1], "field_disc": 522072, "field_disc_factorization": [[2, 3], [3, 3], [2417, 1]], "field_poly": [1, 5, -12, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.864", "prec": 17}, {"__RealLiteral__": 0, "data": "0.330", "prec": 17}, {"__RealLiteral__": 0, "data": "40.559", "prec": 20}, {"__RealLiteral__": 0, "data": "15.981", "prec": 20}, {"__RealLiteral__": 0, "data": "632.200", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[7, -1], [11, 1]], "trace_display": [-2, 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