# Stored data for newform 441.6.a.w, downloaded from the LMFDB on 19 April 2024.
{"label": "441.6.a.w", "space_label": "441.6.a", "level": 441, "weight": 6, "hecke_orbit": 23, "hecke_orbit_code": 99079191902814649, "dim": 4, "is_polredabs": true, "trace_hash": 1044045540948737830, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [204, -186, -94, 3, 1]], [5, [-3188244, -302700, -7657, 0, 1]], [13, [149501563456, 515112852, -1148423, -462, 1]]], "qexp_display": "q+(-1+\\beta _{1})q^{2}+(18-\\beta _{1}+\\beta _{2})q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 15876, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 70.72926453752446, "hecke_ring_index": 7, "level_radical": 21, "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": "0.003", "prec": 17}, "analytic_rank_proved": true, "char_values": [441, 1, [344, 199], [1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [3, 7], "conrey_indexes": [1], "field_disc": 1634484444, "field_disc_factorization": [[2, 2], [3, 1], [167, 1], [227, 1], [3593, 1]], "field_poly": [294, 7, -97, -1, 1], "hecke_ring_index_factorization": [[7, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.093", "prec": 17}, {"__RealLiteral__": 0, "data": "3.787", "prec": 17}, {"__RealLiteral__": 0, "data": "0.418", "prec": 17}, {"__RealLiteral__": 0, "data": "41.407", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "703.844", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [7, 1]], "trace_display": [-3, 0, 0, 0], "traces": [0, 4, -3, 0, 69, 0, 0, 0, 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