# Stored data for newform 1728.4.a.bt, downloaded from the LMFDB on 06 May 2024.
{"label": "1728.4.a.bt", "space_label": "1728.4.a", "level": 1728, "weight": 4, "hecke_orbit": 46, "hecke_orbit_code": 202661983298782912, "dim": 2, "is_polredabs": true, "nf_label": "2.2.33.1", "trace_hash": 438279184671212720, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-281, -8, 1]], [7, [-153, -24, 1]], [11, [-1, 1]]], "qexp_display": "q+(4+\\beta )q^{5}+(12+\\beta )q^{7}+q^{11}+(-2^{4}+\\cdots)q^{13}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 27648, "fricke_eigenval": 1, "atkin_lehner_string": "++", "analytic_conductor": 101.95530048991978, "hecke_ring_index": 6, "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": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [1728, 1, [703, 325, 1217], [1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [2, 3], "conrey_indexes": [1], "field_disc": 33, "field_disc_factorization": [[3, 1], [11, 1]], "field_poly": [-8, -1, 1], "hecke_ring_index_factorization": [[2, 1], [3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.050", "prec": 17}, {"__RealLiteral__": 0, "data": "1.927", "prec": 17}, {"__RealLiteral__": 0, "data": "0.226", "prec": 17}, {"__RealLiteral__": 0, "data": "9.413", "prec": 17}, {"__RealLiteral__": 0, "data": "2.096", "prec": 17}, {"__RealLiteral__": 0, "data": "63.508", "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], [3, 1]], "trace_display": [0, 0, 8, 24], "traces": [0, 2, 0, 0, 0, 8, 0, 24, 0, 0, 0, 2, 0, -32, 0, 0, 0, 56, 0, -184, 0, 0, 0, -92, 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