# Stored data for newform 4014.2.a.r, downloaded from the LMFDB on 24 April 2024. {"label": "4014.2.a.r", "space_label": "4014.2.a", "level": 4014, "weight": 2, "hecke_orbit": 18, "hecke_orbit_code": 76561193698856878, "dim": 5, "is_polredabs": true, "nf_label": "5.5.356173.1", "trace_hash": 24476543335511444, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[5, [-20, -54, -41, -4, 5, 1]], [7, [80, 72, -15, -18, 1, 1]], [11, [67, -38, -82, 6, 9, 1]]], "qexp_display": "q+q^{2}+q^{4}+(-1+\\beta _{1}-\\beta _{2})q^{5}+(-\\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": 16056, "fricke_eigenval": 1, "atkin_lehner_string": "--+", "analytic_conductor": 32.05195137134194, "hecke_ring_index": 1, "level_radical": 1338, "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": "0.013", "prec": 17}, "analytic_rank_proved": true, "char_values": [4014, 1, [893, 2233], [1, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 1, "level_primes": [2, 3, 223], "conrey_indexes": [1], "field_disc": 356173, "field_disc_factorization": [[356173, 1]], "field_poly": [-4, 14, 9, -7, -2, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.835", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "66.060", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1399.198", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 5, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, 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