# Stored data for newform 585.2.i.b, downloaded from the LMFDB on 23 April 2024.
{"label": "585.2.i.b", "space_label": "585.2.i", "level": 585, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504149416739401, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1657993997740236490, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [1, -1, 1]], [7, [4, 2, 1]]], "qexp_display": "q+(1-\\zeta_{6})q^{2}+(-1+2\\zeta_{6})q^{3}+\\zeta_{6}q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "i", "char_is_real": false, "Nk2": 2340, "analytic_conductor": 4.671248518244902, "hecke_ring_index": 1, "level_radical": 195, "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": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.015", "prec": 17}, "analytic_rank_proved": true, "char_values": [585, 3, [326, 352, 496], [2, 3, 3]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [3, 5, 13], "conrey_indexes": [196, 391], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.001", "prec": 17}, {"__RealLiteral__": 0, "data": "2.015", "prec": 17}, {"__RealLiteral__": 0, "data": "0.074", "prec": 17}, {"__RealLiteral__": 0, "data": "12.002", "prec": 20}, {"__RealLiteral__": 0, "data": "0.541", "prec": 17}, {"__RealLiteral__": 0, "data": "108.166", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [1, 0, 1, -2], "traces": [0, 2, 1, 0, 1, 1, 3, -2, 6, -6, 2, 1, -3, 1, 2, -3, 1, 4, -3, -6, -1, -6, -1, 0, 0, -1, 2, 0, -4, -5, 0, 1, 5, 3, 2, -4, -3, -10, -3, -3, 3, 0, -6, 8, 2, -3, 0, 2, 3, 3, 1, 0, -1, 28, -9, 2, -6, 0, 5, 9, -3, 1, 2, 6, 14, -1, 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"fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "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], [1, -1], [-1, 2], [0, 1], [0, 1], [1, 1], [-2, 2], [3, 0], [-3, 0], [1, 0], [1, -1], [-2, 1], [0, 1], [0, 2], [-2, 1], [1, -1], [2, 0], [-3, 3], [-3, 0], [-1, 1], [-2, -2], [0, -1], [0, 0], [-3, 6], [-1, 1], [1, 0], [3, -6], [-2, 0], [-5, 5], [-1, 2], [0, 1], [0, 5], [1, 1], [2, -2], [-2, 0], [0, -3], [-5, 0], [-3, 3], [-2, 1], [0, 3], [0, 0], [-4, 2], [8, -8], [1, 0], [0, -3], [0, 0], [2, -2], [1, 1], [0, 3], [0, 1], [-2, 4], [-1, 1], [14, 0], [-3, -3], [1, 0], [-6, 6], [3, -6], [0, 5], [0, 9], [-1, -1], [1, -1], [1, 0], [6, -6], [7, 0], [-1, 1], [2, -1], [0, -14], [0, 2], [0, 0], [-2, 2], [0, 0], [-9, 0], [6, 0], [-5, 5], [-1, -1], [0, 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