# Stored data for newform 336.4.a.f, downloaded from the LMFDB on 19 April 2024.
{"label": "336.4.a.f", "space_label": "336.4.a", "level": 336, "weight": 4, "hecke_orbit": 6, "hecke_orbit_code": 22517998203961680, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 898372884152776645, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [18, 1]], [11, [-36, 1]]], "qexp_display": "q+3q^{3}-18q^{5}-7q^{7}+9q^{9}+6^{2}q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 5376, "fricke_eigenval": 1, "atkin_lehner_string": "--+", "analytic_conductor": 19.824641761928845, "hecke_ring_index": 1, "level_radical": 42, "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": [336, 1, [127, 85, 113, 241], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 7], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.987", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.982", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.967", "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], [7, 1]], "trace_display": [0, 3, -18, -7], "traces": [0, 1, 0, 3, 0, -18, 0, -7, 0, 9, 0, 36, 0, -34, 0, -54, 0, 42, 0, 124, 0, -21, 0, 0, 0, 199, 0, 27, 0, 102, 0, 160, 0, 108, 0, 126, 0, 398, 0, -102, 0, -318, 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