# Stored data for newform 3969.2.a.w, downloaded from the LMFDB on 28 March 2024. {"label": "3969.2.a.w", "space_label": "3969.2.a", "level": 3969, "weight": 2, "hecke_orbit": 23, "hecke_orbit_code": 99079191835709313, "dim": 4, "is_polredabs": true, "nf_label": "4.4.14013.1", "trace_hash": 2140947859853805504, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [3, 6, -6, -1, 1]], [5, [-21, -33, -12, 2, 1]], [11, [-249, 174, -24, -5, 1]], [13, [-7, 20, 0, -5, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+(1+\\beta _{2})q^{4}+(-1+\\beta _{1}+\\beta _{2}+\\cdots)q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 15876, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 31.692624562246184, "hecke_ring_index": 1, "level_radical": 21, "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": "0.005", "prec": 17}, "analytic_rank_proved": true, "char_values": [3969, 1, [2108, 3727], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 7], "conrey_indexes": [1], "field_disc": 14013, "field_disc_factorization": [[3, 4], [173, 1]], "field_poly": [3, 6, -6, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.098", "prec": 17}, {"__RealLiteral__": 0, "data": "3.722", "prec": 17}, {"__RealLiteral__": 0, "data": "0.667", "prec": 17}, {"__RealLiteral__": 0, "data": "36.711", "prec": 20}, {"__RealLiteral__": 0, "data": "6.073", "prec": 17}, {"__RealLiteral__": 0, "data": "526.293", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c1", 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