# Stored data for newform 1344.4.a.bg, downloaded from the LMFDB on 19 April 2024.
{"label": "1344.4.a.bg", "space_label": "1344.4.a", "level": 1344, "weight": 4, "hecke_orbit": 33, "hecke_orbit_code": 144115188142966080, "dim": 2, "is_polredabs": true, "nf_label": "2.2.57.1", "trace_hash": 362280897639302492, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[5, [-48, 6, 1]], [11, [-1416, -6, 1]]], "qexp_display": "q-3q^{3}+(-3-\\beta )q^{5}+7q^{7}+9q^{9}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 21504, "fricke_eigenval": -1, "atkin_lehner_string": "++-", "analytic_conductor": 79.29856704771538, "hecke_ring_index": 2, "level_radical": 42, "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": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [1344, 1, [127, 1093, 449, 577], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [2, 3, 7], "conrey_indexes": [1], "field_disc": 57, "field_disc_factorization": [[3, 1], [19, 1]], "field_poly": [-14, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.967", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.260", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "61.132", "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], [7, -1]], "trace_display": [0, -6, -6, 14], "traces": [0, 2, 0, -6, 0, -6, 0, 14, 0, 18, 0, 6, 0, -16, 0, 18, 0, -6, 0, -64, 0, -42, 0, 6, 0, -118, 0, 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