# Stored data for newform 4005.2.a.x, downloaded from the LMFDB on 24 April 2024.
{"label": "4005.2.a.x", "space_label": "4005.2.a", "level": 4005, "weight": 2, "hecke_orbit": 24, "hecke_orbit_code": 103582791463079845, "dim": 17, "is_polredabs": true, "trace_hash": 846323035184783923, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [24, -231, 99, 3184, -3066, -7119, 7299, 6279, -7002, -2456, 3371, 320, -849, 45, 105, -15, -5, 1]], [7, [-2654208, -4003776, 4643712, 7875408, -3089632, -5627911, 1317270, 1955568, -427474, -355798, 88986, 32862, -10266, -1219, 580, -8, -12, 1]], [11, [18210816, 69894144, 12189696, -90317824, -19357824, 44484096, 7185504, -10775536, -1255896, 1434080, 119712, -109444, -6384, 4744, 178, -108, -2, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+(1+\\beta _{2})q^{4}+q^{5}+(1+\\beta _{8}+\\cdots)q^{7}+\\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": 4, "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": "0.004", "prec": 17}, "analytic_rank_proved": true, "char_values": [4005, 1, [3116, 802, 181], [1, 1, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 1, "level_primes": [3, 5, 89], "conrey_indexes": [1], "field_disc": 2111123926621975763498954496433127424, "field_disc_factorization": [[2, 16], [3, 3], [11, 2], [821, 1], [522127, 1], [1156429, 1], [1860559, 1], [10690621, 1]], "field_poly": [24, -231, 99, 3184, -3066, -7119, 7299, 6279, -7002, -2456, 3371, 320, -849, 45, 105, -15, -5, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.224", "prec": 17}, {"__RealLiteral__": 0, 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