# Stored data for newform 378.4.a.f, downloaded from the LMFDB on 04 May 2024.
{"label": "378.4.a.f", "space_label": "378.4.a", "level": 378, "weight": 4, "hecke_orbit": 6, "hecke_orbit_code": 22517998203961722, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1906182376651827845, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[5, [-15, 1]], [11, [42, 1]]], "qexp_display": "q-2q^{2}+4q^{4}+15q^{5}+7q^{7}-8q^{8}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 6048, "fricke_eigenval": -1, "atkin_lehner_string": "++-", "analytic_conductor": 22.302721982169952, "hecke_ring_index": 1, "level_radical": 42, "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": 0, "analytic_rank_proved": true, "char_values": [378, 1, [29, 325], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 7], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.008", "prec": 17}, {"__RealLiteral__": 0, "data": "0.962", "prec": 17}, {"__RealLiteral__": 0, "data": "0.028", "prec": 17}, {"__RealLiteral__": 0, "data": "1.882", "prec": 17}, {"__RealLiteral__": 0, "data": "0.111", "prec": 17}, {"__RealLiteral__": 0, "data": "4.700", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [3, 1], [7, -1]], "trace_display": [-2, 0, 15, 7], "traces": [0, 1, -2, 0, 4, 15, 0, 7, -8, 0, -30, -42, 0, -88, -14, 0, 16, -45, 0, -106, 60, 0, 84, 114, 0, 100, 176, 0, 28, 66, 0, -304, -32, 0, 90, 105, 0, -187, 212, 0, -120, 69, 0, 29, -168, 0, -228, 471, 0, 49, -200, 0, -352, 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