# Stored data for newform 4009.2.a.b, downloaded from the LMFDB on 19 April 2024.
{"label": "4009.2.a.b", "space_label": "4009.2.a", "level": 4009, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660928937, "dim": 3, "is_polredabs": true, "nf_label": "3.3.49.1", "trace_hash": 740133168041177781, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [1, -1, -2, 1]]], "qexp_display": "q+(1-\\beta _{1})q^{2}+(-1+\\beta _{1})q^{3}+(1-2\\beta _{1}+\\cdots)q^{4}+\\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": 14, "field_poly_is_real_cyclotomic": true, "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": "0.005", "prec": 17}, "analytic_rank_proved": true, "char_values": [4009, 1, [2111, 1901], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [19, 211], "conrey_indexes": [1], "field_disc": 49, "field_disc_factorization": [[7, 2]], "field_poly": [1, -2, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.962", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "22.088", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "241.195", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[19, -1], [211, -1]], "trace_display": [2, -2, -3, 3], "traces": [0, 3, 2, -2, 0, -3, -6, 3, 3, -3, -2, 1, -7, 0, 9, 2, 2, -2, 5, 3, -7, -9, -4, 2, -2, 2, 0, 1, 7, 6, 13, 5, -7, 4, 1, 4, 14, 9, 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