# Stored data for newform 784.4.a.u, downloaded from the LMFDB on 19 April 2024.
{"label": "784.4.a.u", "space_label": "784.4.a", "level": 784, "weight": 4, "hecke_orbit": 21, "hecke_orbit_code": 90071992614519568, "dim": 2, "is_polredabs": true, "nf_label": "2.2.37.1", "trace_hash": 1668875069778664306, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[3, [-37, 0, 1]], [5, [-99, 14, 1]]], "qexp_display": "q-\\beta q^{3}+(-7-2\\beta )q^{5}+10q^{9}+(-2^{4}+\\cdots)q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 12544, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 46.25749744450064, "hecke_ring_index": 2, "level_radical": 14, "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": "0.003", "prec": 17}, "analytic_rank_proved": true, "char_values": [784, 1, [687, 197, 689], [1, 1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [2, 7], "conrey_indexes": [1], "field_disc": 37, "field_disc_factorization": [[37, 1]], "field_poly": [-9, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.001", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.940", "prec": 17}, {"__RealLiteral__": 0, "data": "1.349", "prec": 17}, {"__RealLiteral__": 0, "data": "69.570", "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], [7, 1]], "trace_display": [0, 0, -14, 0], "traces": [0, 2, 0, 0, 0, -14, 0, 0, 0, 20, 0, -32, 0, -28, 0, 148, 0, -154, 0, 224, 0, 0, 0, -68, 0, 144, 0, 0, 0, -236, 0, 196, 0, -518, 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