# Stored data for newform 4005.2.a.m, downloaded from the LMFDB on 25 April 2024.
{"label": "4005.2.a.m", "space_label": "4005.2.a", "level": 4005, "weight": 2, "hecke_orbit": 13, "hecke_orbit_code": 54043195562004389, "dim": 4, "is_polredabs": true, "nf_label": "4.4.2777.1", "trace_hash": 1939059674227504174, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [4, -1, -5, 0, 1]], [7, [-4, 5, 14, 7, 1]], [11, [64, 8, -20, 0, 1]]], "qexp_display": "q-\\beta _{2}q^{2}+(1-\\beta _{3})q^{4}+q^{5}+(-2+\\beta _{1}+\\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": 16020, "fricke_eigenval": 1, "atkin_lehner_string": "--+", "analytic_conductor": 31.980086009522793, "hecke_ring_index": 1, "level_radical": 1335, "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": "0.009", "prec": 17}, "analytic_rank_proved": true, "char_values": [4005, 1, [3116, 802, 181], [1, 1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 5, 89], "conrey_indexes": [1], "field_disc": 2777, "field_disc_factorization": [[2777, 1]], "field_poly": [2, 1, -4, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.749", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "36.772", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "542.345", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, -1], [89, 1]], "trace_display": [0, 0, 4, -7], "traces": [0, 4, 0, 0, 2, 4, 0, -7, 3, 0, 0, 0, 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