# Stored data for newform 4008.2.a.h, downloaded from the LMFDB on 18 April 2024. {"label": "4008.2.a.h", "space_label": "4008.2.a", "level": 4008, "weight": 2, "hecke_orbit": 8, "hecke_orbit_code": 31525197425151912, "dim": 8, "is_polredabs": true, "trace_hash": 611619553587443831, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[5, [269, 4, -418, 13, 163, -3, -23, 0, 1]], [7, [45, -188, -253, 166, 181, -39, -30, 1, 1]]], "qexp_display": "q-q^{3}+\\beta _{1}q^{5}+\\beta _{3}q^{7}+q^{9}+(\\beta _{2}+\\beta _{4}+\\cdots)q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 16032, "fricke_eigenval": 1, "atkin_lehner_string": "-+-", "analytic_conductor": 32.00404113012918, "hecke_ring_index": 1, "level_radical": 1002, "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": "0.003", "prec": 17}, "analytic_rank_proved": true, "char_values": [4008, 1, [3007, 2005, 1337, 673], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 1, "level_primes": [2, 3, 167], "conrey_indexes": [1], "field_disc": 13493468617364, "field_disc_factorization": [[2, 2], [1051, 1], [3209673791, 1]], "field_poly": [269, 4, -418, 13, 163, -3, -23, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.123", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "144.995", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4586.805", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": 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