# Stored data for newform 4005.2.a.o, downloaded from the LMFDB on 25 April 2024.
{"label": "4005.2.a.o", "space_label": "4005.2.a", "level": 4005, "weight": 2, "hecke_orbit": 15, "hecke_orbit_code": 63050394816745381, "dim": 7, "is_polredabs": true, "trace_hash": 1977398637721938687, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [9, 6, -29, -8, 24, -3, -4, 1]], [7, [4, -76, -96, 189, 236, 94, 16, 1]], [11, [128, -608, 968, -639, 149, 14, -10, 1]]], "qexp_display": "q+(1-\\beta _{1})q^{2}+(2-\\beta _{1}+\\beta _{3})q^{4}-q^{5}+\\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": "0.005", "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": 324323556, "field_disc_factorization": [[2, 2], [3, 1], [27026963, 1]], "field_poly": [6, -12, -10, 19, 6, -8, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.087", "prec": 17}, {"__RealLiteral__": 0, "data": "6.315", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "118.541", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3524.717", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 7, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, 1], [89, 1]], "trace_display": [4, 0, -7, -16], 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