# Stored data for newform 1638.2.a.r, downloaded from the LMFDB on 07 May 2024.
{"label": "1638.2.a.r", "space_label": "1638.2.a", "level": 1638, "weight": 2, "hecke_orbit": 18, "hecke_orbit_code": 76561193698854502, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1481122248538840621, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-1, 1]], [11, [-1, 1]], [17, [-1, 1]], [19, [-7, 1]]], "qexp_display": "q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 6552, "fricke_eigenval": -1, "atkin_lehner_string": "--+-", "analytic_conductor": 13.079495851085728, "hecke_ring_index": 1, "level_radical": 546, "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": "0.011", "prec": 17}, "analytic_rank_proved": true, "char_values": [1638, 1, [911, 703, 379], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 7, 13], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.037", "prec": 17}, {"__RealLiteral__": 0, "data": "1.016", "prec": 17}, {"__RealLiteral__": 0, "data": "0.053", "prec": 17}, {"__RealLiteral__": 0, "data": "2.093", "prec": 17}, {"__RealLiteral__": 0, "data": "0.107", "prec": 17}, {"__RealLiteral__": 0, "data": "5.323", "prec": 17}], "related_objects": ["EllipticCurve/Q/1638/r"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, -1], [7, 1], [13, -1]], "trace_display": [1, 0, 1, -1], "traces": [0, 1, 1, 0, 1, 1, 0, -1, 1, 0, 1, 1, 0, 1, -1, 0, 1, 1, 0, 7, 1, 0, 1, -3, 0, -4, 1, 0, -1, 3, 0, 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