# Stored data for newform 261.4.a.f, downloaded from the LMFDB on 20 April 2024.
{"label": "261.4.a.f", "space_label": "261.4.a", "level": 261, "weight": 4, "hecke_orbit": 6, "hecke_orbit_code": 22517998203961605, "dim": 5, "is_polredabs": true, "nf_label": "5.5.13458092.1", "trace_hash": 550308152207061075, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [256, 192, -28, -33, 0, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+(6+2\\beta _{1}+2\\beta _{3}+\\beta _{4})q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 4176, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 15.399498511498301, "hecke_ring_index": 4, "level_radical": 87, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [261, 1, [146, 118], [1, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 1, "level_primes": [3, 29], "conrey_indexes": [1], "field_disc": 13458092, "field_disc_factorization": [[2, 2], [31, 1], [108533, 1]], "field_poly": [-8, 20, 18, -14, -1, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.055", "prec": 17}, {"__RealLiteral__": 0, "data": "4.573", "prec": 17}, {"__RealLiteral__": 0, "data": "0.816", "prec": 17}, {"__RealLiteral__": 0, "data": "57.774", "prec": 20}, {"__RealLiteral__": 0, "data": "6.512", "prec": 17}, {"__RealLiteral__": 0, "data": "1163.351", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 5, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [29, -1]], "trace_display": [0, 0, -10, 40], "traces": [0, 5, 0, 0, 26, -10, 0, 40, 84, 0, -64, -12, 0, 14, 192, 0, 146, -66, 0, 214, -6, 0, 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