# Stored data for newform 384.8.a.s, downloaded from the LMFDB on 25 April 2024.
{"label": "384.8.a.s", "space_label": "384.8.a", "level": 384, "weight": 8, "hecke_orbit": 19, "hecke_orbit_code": 81064793426887040, "dim": 4, "is_polredabs": true, "trace_hash": 2244497249186574374, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [2983276800, 22830080, -233184, -192, 1]], [7, [-37318092656, 407076832, -627336, -680, 1]]], "qexp_display": "q+3^{3}q^{3}+(48+\\beta _{2})q^{5}+(170+\\beta _{3})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": 98304, "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": 3012610560, "field_disc_factorization": [[2, 9], [3, 1], [5, 1], [392267, 1]], "field_poly": [12138, -2448, -430, 0, 1], "hecke_ring_index_factorization": [[2, 15], [3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.073", "prec": 17}, {"__RealLiteral__": 0, "data": "3.905", "prec": 17}, {"__RealLiteral__": 0, "data": "0.672", "prec": 17}, {"__RealLiteral__": 0, "data": "41.561", "prec": 20}, {"__RealLiteral__": 0, "data": "9.240", "prec": 17}, {"__RealLiteral__": 0, "data": "672.046", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "7.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, -1]], "trace_display": [0, 108, 192, 680], "traces": [0, 4, 0, 108, 0, 192, 0, 680, 0, 2916, 0, -4496, 0, -12840, 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