# Stored data for newform 1421.4.a.e, downloaded from the LMFDB on 19 April 2024.
{"label": "1421.4.a.e", "space_label": "1421.4.a", "level": 1421, "weight": 4, "hecke_orbit": 5, "hecke_orbit_code": 18014398576592269, "dim": 5, "is_polredabs": true, "nf_label": "5.5.13458092.1", "trace_hash": 295434173781703388, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-256, 192, 28, -33, 0, 1]], [3, [1042, 187, -322, -52, 8, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+(-1+\\beta _{1}+\\beta _{3}+\\beta _{4})q^{3}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 22736, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 83.84171411815741, "hecke_ring_index": 4, "level_radical": 203, "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": [1421, 1, [1277, 785], [1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [7, 29], "conrey_indexes": [1], "field_disc": 13458092, "field_disc_factorization": [[2, 2], [31, 1], [108533, 1]], "field_poly": [-8, 20, 18, -14, -1, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.571", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "57.759", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1163.265", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 5, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[7, -1], [29, 1]], "trace_display": [0, -8, -10, 0], "traces": [0, 5, 0, -8, 26, -10, -34, 0, -84, 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