# Stored data for newform 768.4.a.f, downloaded from the LMFDB on 20 April 2024.
{"label": "768.4.a.f", "space_label": "768.4.a", "level": 768, "weight": 4, "hecke_orbit": 6, "hecke_orbit_code": 22517998203962112, "dim": 2, "is_polredabs": true, "nf_label": "2.2.12.1", "trace_hash": 1596061623079619104, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-12, 0, 1]], [7, [-588, 0, 1]], [11, [48, 1]], [19, [-4, 1]]], "qexp_display": "q-3q^{3}+\\beta q^{5}+7\\beta q^{7}+9q^{9}-48q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 12288, "fricke_eigenval": 1, "atkin_lehner_string": "++", "analytic_conductor": 45.31346688440879, "hecke_ring_index": 2, "level_radical": 6, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 12, "field_poly_is_real_cyclotomic": true, "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": "0.507", "prec": 17}, "analytic_rank_proved": true, "char_values": [768, 1, [511, 517, 257], [1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [1], "field_disc": 12, "field_disc_factorization": [[2, 2], [3, 1]], "field_poly": [-3, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.031", "prec": 17}, {"__RealLiteral__": 0, "data": "1.913", "prec": 17}, {"__RealLiteral__": 0, "data": "0.310", "prec": 17}, {"__RealLiteral__": 0, "data": "14.881", "prec": 20}, {"__RealLiteral__": 0, "data": "3.166", "prec": 17}, {"__RealLiteral__": 0, "data": "144.565", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [3, 1]], "trace_display": [0, -6, 0, 0], "traces": [0, 2, 0, -6, 0, 0, 0, 0, 0, 18, 0, -96, 0, 0, 0, 0, 0, 108, 0, 8, 0, 0, 0, 0, 0, -226, 0, -54, 0, 0, 0, 0, 0, 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