# Stored data for newform 4005.2.a.r, downloaded from the LMFDB on 16 April 2024.
{"label": "4005.2.a.r", "space_label": "4005.2.a", "level": 4005, "weight": 2, "hecke_orbit": 18, "hecke_orbit_code": 76561193698856869, "dim": 10, "is_polredabs": true, "trace_hash": 805332772131945453, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [-9, -77, -178, -11, 234, 106, -76, -53, 1, 6, 1]], [7, [7112, 16079, -57338, 26687, 6423, -5463, 154, 346, -37, -7, 1]], [11, [3328, -5696, -20928, 37392, 5224, -8264, -4, 540, -36, -10, 1]]], "qexp_display": "q+(-1+\\beta _{1})q^{2}+(2-\\beta _{1}+\\beta _{2})q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 16020, "fricke_eigenval": -1, "atkin_lehner_string": "-++", "analytic_conductor": 31.980086009522793, "hecke_ring_index": 1, "level_radical": 1335, "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": "0.007", "prec": 17}, "analytic_rank_proved": true, "char_values": [4005, 1, [3116, 802, 181], [1, 1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 5, 89], "conrey_indexes": [1], "field_disc": 114767250476174912, "field_disc_factorization": [[2, 6], [7, 1], [11, 1], [23288808944029, 1]], "field_poly": [2, -39, 29, 106, -57, -103, 29, 35, -8, -4, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.138", "prec": 17}, {"__RealLiteral__": 0, "data": "8.726", "prec": 17}, {"__RealLiteral__": 0, "data": "5.630", "prec": 17}, {"__RealLiteral__": 0, "data": "226.289", "prec": 24}, {"__RealLiteral__": 0, "data": "352.473", "prec": 24}, {"__RealLiteral__": 0, "data": "9578.992", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 10, 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