# Stored data for newform 464.4.a.d, downloaded from the LMFDB on 23 April 2024.
{"label": "464.4.a.d", "space_label": "464.4.a", "level": 464, "weight": 4, "hecke_orbit": 4, "hecke_orbit_code": 13510798949220816, "dim": 2, "is_polredabs": true, "nf_label": "2.2.13.1", "trace_hash": 1521205187505160646, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[3, [-13, 0, 1]]], "qexp_display": "q-\\beta q^{3}+(-5-2\\beta )q^{5}+(10+4\\beta )q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 7424, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 27.376886242663645, "hecke_ring_index": 2, "level_radical": 58, "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": [464, 1, [175, 117, 321], [1, 1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [2, 29], "conrey_indexes": [1], "field_disc": 13, "field_disc_factorization": [[13, 1]], "field_poly": [-3, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.950", "prec": 17}, {"__RealLiteral__": 0, "data": "0.262", "prec": 17}, {"__RealLiteral__": 0, "data": "9.467", "prec": 17}, {"__RealLiteral__": 0, "data": "3.169", "prec": 17}, {"__RealLiteral__": 0, "data": "64.341", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [29, 1]], "trace_display": [0, 0, -10, 20], "traces": [0, 2, 0, 0, 0, -10, 0, 20, 0, -28, 0, 32, 0, -54, 0, 52, 0, -44, 0, 32, 0, -104, 0, 36, 0, -96, 0, 0, 0, -58, 0, -20, 0, -26, 0, -308, 0, -144, 0, -156, 0, 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