# Stored data for newform 3744.2.a.t, downloaded from the LMFDB on 25 April 2024. {"label": "3744.2.a.t", "space_label": "3744.2.a", "level": 3744, "weight": 2, "hecke_orbit": 20, "hecke_orbit_code": 85568392953597600, "dim": 2, "is_polredabs": true, "nf_label": "2.2.8.1", "trace_hash": 2239223581862254645, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[5, [0, 1]], [7, [-8, 0, 1]], [11, [-8, 0, 1]], [29, [4, 1]]], "qexp_display": "q+\\beta q^{7}-\\beta q^{11}-q^{13}+\\beta q^{19}-2\\beta q^{23}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 14976, "fricke_eigenval": 1, "atkin_lehner_string": "+++", "analytic_conductor": 29.895990516767377, "hecke_ring_index": 2, "level_radical": 78, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 8, "field_poly_is_real_cyclotomic": true, "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": "0.514", "prec": 17}, "analytic_rank_proved": true, "char_values": [3744, 1, [703, 2341, 2081, 2017], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 13], "conrey_indexes": [1], "field_disc": 8, "field_disc_factorization": [[2, 3]], "field_poly": [-2, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.965", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "15.574", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "154.623", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [3, 1], [13, 1]], "trace_display": [0, 0, 0, 0], "traces": 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