# Stored data for newform 4032.3.d.i, downloaded from the LMFDB on 25 April 2024.
{"label": "4032.3.d.i", "space_label": "4032.3.d", "level": 4032, "weight": 3, "hecke_orbit": 9, "hecke_orbit_code": 36029003227729856, "dim": 4, "is_polredabs": true, "nf_label": "4.0.12544.1", "trace_hash": 833455345845841808, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [2916, 0, 116, 0, 1]], [11, [46656, 0, 464, 0, 1]], [19, [20, 1]]], "qexp_display": "q+(2\\beta _{1}-\\beta _{3})q^{5}-\\beta _{2}q^{7}+(4\\beta _{1}-2\\beta _{3})q^{11}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "d", "char_is_real": true, "Nk2": 36288, "analytic_conductor": 109.8640425900717, "hecke_ring_index": 6, "level_radical": 42, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.510", "prec": 17}, "analytic_rank_proved": true, "char_values": [4032, 2, [127, 3781, 1793, 577], [2, 2, 1, 2]], "hecke_ring_generator_nbound": 17, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [449], "field_disc": 12544, "field_disc_factorization": [[2, 8], [7, 2]], "field_poly": [9, 0, 8, 0, 1], "hecke_ring_index_factorization": [[2, 1], [3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.034", "prec": 17}, {"__RealLiteral__": 0, "data": "3.839", "prec": 17}, {"__RealLiteral__": 0, "data": "1.508", "prec": 17}, {"__RealLiteral__": 0, "data": "74.335", "prec": 20}, {"__RealLiteral__": 0, "data": "70.604", "prec": 20}, {"__RealLiteral__": 0, "data": "2052.683", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, -132, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 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