# Stored data for newform 4005.2.a.p, downloaded from the LMFDB on 23 April 2024.
{"label": "4005.2.a.p", "space_label": "4005.2.a", "level": 4005, "weight": 2, "hecke_orbit": 16, "hecke_orbit_code": 67553994444115877, "dim": 8, "is_polredabs": true, "trace_hash": 931924109619399694, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-1, -11, -27, 19, 34, -9, -11, 1, 1]], [7, [-676, -856, 244, 536, 11, -102, -12, 6, 1]], [11, [-2752, 704, 2192, -112, -599, -75, 50, 14, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+(1-\\beta _{1}-\\beta _{3}-\\beta _{4}+\\beta _{5}+\\cdots)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": 2, "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": "0.003", "prec": 17}, "analytic_rank_proved": true, "char_values": [4005, 1, [3116, 802, 181], [1, 1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 1, "level_primes": [3, 5, 89], "conrey_indexes": [1], "field_disc": 44622944512, "field_disc_factorization": [[2, 8], [2687, 1], [64871, 1]], "field_poly": [-1, 11, -27, -19, 34, 9, -11, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "6.877", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "139.709", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4710.976", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": 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