# Stored data for newform 1728.4.a.z, downloaded from the LMFDB on 19 April 2024.
{"label": "1728.4.a.z", "space_label": "1728.4.a", "level": 1728, "weight": 4, "hecke_orbit": 26, "hecke_orbit_code": 112589990751372992, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 603554325207214550, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[5, [-9, 1]], [7, [-1, 1]], [11, [63, 1]]], "qexp_display": "q+9q^{5}+q^{7}-63q^{11}+28q^{13}-72q^{17}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 27648, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 101.95530048991978, "hecke_ring_index": 1, "level_radical": 6, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [1728, 1, [703, 325, 1217], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.984", "prec": 17}, {"__RealLiteral__": 0, "data": "0.007", "prec": 17}, {"__RealLiteral__": 0, "data": "1.956", "prec": 17}, {"__RealLiteral__": 0, "data": "0.037", "prec": 17}, {"__RealLiteral__": 0, "data": "4.876", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, 1]], "trace_display": [0, 0, 9, 1], "traces": [0, 1, 0, 0, 0, 9, 0, 1, 0, 0, 0, -63, 0, 28, 0, 0, 0, -72, 0, 98, 0, 0, 0, 126, 0, -44, 0, 0, 0, -126, 0, 259, 0, 0, 0, 9, 0, -386, 0, 0, 0, 450, 0, 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