# Stored data for newform 1849.4.a.f, downloaded from the LMFDB on 25 April 2024.
{"label": "1849.4.a.f", "space_label": "1849.4.a", "level": 1849, "weight": 4, "hecke_orbit": 6, "hecke_orbit_code": 22517998203963193, "dim": 10, "is_polredabs": true, "trace_hash": 913264946365436548, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-768, -320, 22676, 2180, -9389, -541, 1187, 42, -59, -1, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+\\beta _{5}q^{3}+(4+\\beta _{2})q^{4}+(-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": 29584, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 109.0945316006144, "hecke_ring_index": 8, "level_radical": 43, "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": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [1849, 1, [3], [1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [43], "conrey_indexes": [1], "field_disc": 15571547701878613378283305872, "field_disc_factorization": [[2, 4], [3, 1], [7, 3], [3881, 1], [1573529297, 1], [154873797389, 1]], "field_poly": [-768, -320, 22676, 2180, -9389, -541, 1187, 42, -59, -1, 1], "hecke_ring_index_factorization": [[2, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.195", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "230.450", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "8524.618", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 10, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[43, -1]], "trace_display": [1, -5, -19, 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