# Stored data for newform 3969.2.a.s, downloaded from the LMFDB on 19 April 2024.
{"label": "3969.2.a.s", "space_label": "3969.2.a", "level": 3969, "weight": 2, "hecke_orbit": 19, "hecke_orbit_code": 81064793326227329, "dim": 4, "is_polredabs": true, "nf_label": "4.4.14013.1", "trace_hash": 2144078086787412940, "analytic_rank": 1, "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": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.722", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "36.711", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "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", "atkin_lehner_eigenvals": [[3, 1], [7, 1]], "trace_display": [-1, 0, -2, 0], "traces": [0, 4, -1, 0, 5, -2, 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