# Stored data for newform 441.4.e.i, downloaded from the LMFDB on 29 March 2024. {"label": "441.4.e.i", "space_label": "441.4.e", "level": 441, "weight": 4, "hecke_orbit": 9, "hecke_orbit_code": 36029071963980217, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 486245048953252831, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [0, 1]], [5, [0, 1]], [13, [70, 1]]], "qexp_display": "q+(8-8\\zeta_{6})q^{4}-70q^{13}-2^{6}\\zeta_{6}q^{16}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "e", "char_is_real": false, "Nk2": 7056, "analytic_conductor": 26.019842312531612, "hecke_ring_index": 1, "level_radical": 21, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": 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"artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [0, 0], [0, 0], [8, -8], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-70, 0], [0, 0], [0, 0], [0, -64], [0, 0], [0, 0], [0, -56], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [125, -125], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-308, 308], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -110], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-520, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-560, 560], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -182], [0, 0], [0, 0], [-512, 0], [0, 0], [0, 0], [880, -880], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-1190, 1190], [0, 0], [0, 0], [-448, 0], [0, 0], [0, 0], [0, -884], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], 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