# Stored data for newform 4005.2.a.i, downloaded from the LMFDB on 19 April 2024.
{"label": "4005.2.a.i", "space_label": "4005.2.a", "level": 4005, "weight": 2, "hecke_orbit": 9, "hecke_orbit_code": 36028797052522405, "dim": 3, "is_polredabs": true, "nf_label": "3.3.81.1", "trace_hash": 712184301465984944, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [-1, -3, 0, 1]], [7, [3, 0, -3, 1]], [11, [8, 0, -6, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+\\beta _{2}q^{4}-q^{5}+(1+\\beta _{2})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": 1, "level_radical": 1335, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 18, "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": "0.022", "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": 81, "field_disc_factorization": [[3, 4]], "field_poly": [-1, -3, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.056", "prec": 17}, {"__RealLiteral__": 0, "data": "2.871", "prec": 17}, {"__RealLiteral__": 0, "data": "0.206", "prec": 17}, {"__RealLiteral__": 0, "data": "22.035", "prec": 20}, {"__RealLiteral__": 0, "data": "1.423", "prec": 17}, {"__RealLiteral__": 0, "data": "247.484", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, 1], [89, 1]], "trace_display": [0, 0, -3, 3], "traces": [0, 3, 0, 0, 0, -3, 0, 3, 3, 0, 0, 6, 0, -3, 3, 0, -6, 9, 0, 0, 0, 0, -6, 0, 0, 3, 3, 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