# Stored data for newform 441.4.a.s, downloaded from the LMFDB on 23 April 2024.
{"label": "441.4.a.s", "space_label": "441.4.a", "level": 441, "weight": 4, "hecke_orbit": 19, "hecke_orbit_code": 81064793359778233, "dim": 3, "is_polredabs": true, "nf_label": "3.3.57516.1", "trace_hash": 249690033265950912, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-6, -24, 1, 1]], [5, [-1236, -192, 11, 1]], [13, [18452, 425, -62, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+(8+\\beta _{1}+\\beta _{2})q^{4}+(-4+\\beta _{1}+\\cdots)q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 7056, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 26.019842312531612, "hecke_ring_index": 1, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [441, 1, [344, 199], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 7], "conrey_indexes": [1], "field_disc": 57516, "field_disc_factorization": [[2, 2], [3, 1], [4793, 1]], "field_poly": [6, -24, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.852", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "21.781", "prec": 20}, {"__RealLiteral__": 0, "data": "1.358", "prec": 17}, {"__RealLiteral__": 0, "data": "254.753", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [7, 1]], "trace_display": [-1, 0, -11, 0], "traces": [0, 3, -1, 0, 25, -11, 0, 0, -39, 0, -55, -35, 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