# Stored data for newform 384.8.a.l, downloaded from the LMFDB on 25 April 2024.
{"label": "384.8.a.l", "space_label": "384.8.a", "level": 384, "weight": 8, "hecke_orbit": 12, "hecke_orbit_code": 49539596035293568, "dim": 3, "is_polredabs": true, "trace_hash": 655548800019863070, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [23304000, -85520, -308, 1]], [7, [765563000, -1837620, -6, 1]]], "qexp_display": "q+3^{3}q^{3}+(103+\\beta _{1})q^{5}+(2+\\beta _{2})q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 24576, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 119.95584978590276, "hecke_ring_index": 768, "level_radical": 6, "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": [384, 1, [127, 133, 257], [1, 1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 1, "level_primes": [2, 3], "conrey_indexes": [1], "field_disc": 4342456, "field_disc_factorization": [[2, 3], [149, 1], [3643, 1]], "field_poly": [-1680, -286, 0, 1], "hecke_ring_index_factorization": [[2, 8], [3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.025", "prec": 17}, {"__RealLiteral__": 0, "data": "2.928", "prec": 17}, {"__RealLiteral__": 0, "data": "0.189", "prec": 17}, {"__RealLiteral__": 0, "data": "22.420", "prec": 20}, {"__RealLiteral__": 0, "data": "3.611", "prec": 17}, {"__RealLiteral__": 0, "data": "245.799", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "7.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, -1]], "trace_display": [0, 81, 308, 6], "traces": [0, 3, 0, 81, 0, 308, 0, 6, 0, 2187, 0, 1468, 0, 3070, 0, 8316, 0, -5126, 0, 14168, 0, 162, 0, 59980, 0, 31529, 0, 59049, 0, 71984, 0, 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