# Stored data for newform 1045.2.a.d, downloaded from the LMFDB on 25 April 2024.
{"label": "1045.2.a.d", "space_label": "1045.2.a", "level": 1045, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13510798915666965, "dim": 5, "is_polredabs": true, "nf_label": "5.5.14641.1", "trace_hash": 1172542378381216330, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [1, -10, -15, -3, 3, 1]]], "qexp_display": "q+(-1+\\beta _{1}-\\beta _{4})q^{2}+(-2-\\beta _{2}+\\beta _{3}+\\cdots)q^{3}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 4180, "fricke_eigenval": 1, "atkin_lehner_string": "-+-", "analytic_conductor": 8.3443670112238, "hecke_ring_index": 1, "level_radical": 1045, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 22, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [1045, 1, [837, 761, 496], [1, 1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [5, 11, 19], "conrey_indexes": [1], "field_disc": 14641, "field_disc_factorization": [[11, 4]], "field_poly": [-1, 3, 3, -4, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.661", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "58.078", "prec": 20}, {"__RealLiteral__": 0, "data": "7.786", "prec": 17}, {"__RealLiteral__": 0, "data": "1043.367", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 5, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[5, -1], [11, 1], [19, -1]], "trace_display": [-3, -7, 5, -11], "traces": [0, 5, -3, -7, 5, 5, 2, -11, 3, 8, -3, -5, -7, 1, 0, -7, -3, -3, -7, 5, 5, 11, 3, -8, 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