# Stored data for newform 441.6.a.f, downloaded from the LMFDB on 23 September 2023.
{"label": "441.6.a.f", "space_label": "441.6.a", "level": 441, "weight": 6, "hecke_orbit": 6, "hecke_orbit_code": 22517998237516217, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 749693333298598637, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [0, 1]], [5, [0, 1]], [13, [-427, 1]]], "qexp_display": "q-2^{5}q^{4}+427q^{13}+2^{10}q^{16}-3143q^{19}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 15876, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 70.72926453752446, "hecke_ring_index": 1, "level_radical": 21, "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": 1, "is_self_dual": true, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.510", "prec": 17}, "analytic_rank_proved": true, "char_values": [441, 1, [344, 199], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 2, "level_primes": [3, 7], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.027", "prec": 17}, {"__RealLiteral__": 0, "data": "0.963", "prec": 17}, {"__RealLiteral__": 0, "data": "0.035", "prec": 17}, {"__RealLiteral__": 0, "data": "2.852", "prec": 17}, {"__RealLiteral__": 0, "data": "0.013", "prec": 17}, {"__RealLiteral__": 0, "data": "9.410", "prec": 17}], "related_objects": [], "self_twist_discs": [-3], "cm_discs": [-3], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "5.2.1.d1", "atkin_lehner_eigenvals": [[3, 1], [7, -1]], "trace_display": [0, 0, 0, 0], "traces": [0, 1, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 427, 0, 0, 1024, 0, 0, -3143, 0, 0, 0, 0, 0, -3125, 0, 0, 0, 0, 0, -2723, 0, 0, 0, 0, 0, -6661, 0, 0, 0, 0, 0, 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