# Stored data for newform 4009.2.a.a, downloaded from the LMFDB on 19 April 2024.
{"label": "4009.2.a.a", "space_label": "4009.2.a", "level": 4009, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 33558441, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1958215047929904490, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [1, 1]]], "qexp_display": "q-q^{2}+2q^{3}-q^{4}+3q^{5}-2q^{6}+3q^{8}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 16036, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 32.0120261703313, "hecke_ring_index": 1, "level_radical": 4009, "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": "0.016", "prec": 17}, "analytic_rank_proved": true, "char_values": [4009, 1, [2111, 1901], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [19, 211], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.031", "prec": 17}, {"__RealLiteral__": 0, "data": "0.968", "prec": 17}, {"__RealLiteral__": 0, "data": "0.064", "prec": 17}, {"__RealLiteral__": 0, "data": "1.879", "prec": 17}, {"__RealLiteral__": 0, "data": "0.142", "prec": 17}, {"__RealLiteral__": 0, "data": "4.570", "prec": 17}], "related_objects": ["EllipticCurve/Q/4009/a"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[19, 1], [211, -1]], "trace_display": [-1, 2, 3, 0], "traces": [0, 1, -1, 2, -1, 3, -2, 0, 3, 1, -3, 0, -2, 4, 0, 6, -1, 0, -1, -1, -3, 0, 0, -1, 6, 4, -4, -4, 0, 3, -6, 4, -5, 0, 0, 0, -1, 0, 1, 8, 9, 10, 0, 6, 0, 3, 1, 0, -2, -7, -4, 0, -4, 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