# Stored data for newform 405.4.a.n, downloaded from the LMFDB on 18 April 2024.
{"label": "405.4.a.n", "space_label": "405.4.a", "level": 405, "weight": 4, "hecke_orbit": 14, "hecke_orbit_code": 58546795222925717, "dim": 7, "is_polredabs": true, "trace_hash": 1457249153588429847, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [288, -1200, -460, 479, 74, -44, -2, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+(5+\\beta _{2})q^{4}+5q^{5}+(3-\\beta _{5}+\\cdots)q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 6480, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 23.89577355232495, "hecke_ring_index": 486, "level_radical": 15, "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": [405, 1, [326, 82], [1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 1, "level_primes": [3, 5], "conrey_indexes": [1], "field_disc": 2327542925397264, "field_disc_factorization": [[2, 4], [3, 3], [9851, 1], [546932377, 1]], "field_poly": [288, -1200, -460, 479, 74, -44, -2, 1], "hecke_ring_index_factorization": [[2, 1], [3, 5]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.038", "prec": 17}, {"__RealLiteral__": 0, "data": "6.225", "prec": 17}, {"__RealLiteral__": 0, "data": "0.396", "prec": 17}, {"__RealLiteral__": 0, "data": "102.647", "prec": 24}, {"__RealLiteral__": 0, "data": "32.449", "prec": 20}, {"__RealLiteral__": 0, "data": "2726.004", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 7, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, -1]], "trace_display": [2, 0, 35, 22], "traces": [0, 7, 2, 0, 36, 35, 0, 22, 18, 0, 10, 23, 0, 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