# Stored data for newform 178.2.a.b, downloaded from the LMFDB on 20 April 2024.
{"label": "178.2.a.b", "space_label": "178.2.a", "level": 178, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660925106, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 2256027418486540454, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [-1, 1]]], "qexp_display": "q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}-4q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 712, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 1.4213371559787908, "hecke_ring_index": 1, "level_radical": 178, "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": "0.017", "prec": 17}, "analytic_rank_proved": true, "char_values": [178, 1, [3], [1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 89], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.025", "prec": 17}, {"__RealLiteral__": 0, "data": "0.981", "prec": 17}, {"__RealLiteral__": 0, "data": "0.093", "prec": 17}, {"__RealLiteral__": 0, "data": "1.936", "prec": 17}, {"__RealLiteral__": 0, "data": "0.290", "prec": 17}, {"__RealLiteral__": 0, "data": "4.816", "prec": 17}], "related_objects": ["EllipticCurve/Q/178/b"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [89, 1]], "trace_display": [1, 1, 3, -4], "traces": [0, 1, 1, 1, 1, 3, 1, -4, 1, -2, 3, -6, 1, 2, -4, 3, 1, 3, -2, 5, 3, -4, -6, -3, 1, 4, 2, -5, -4, 0, 3, 5, 1, -6, 3, -12, -2, -10, 5, 2, 3, 0, -4, -1, -6, -6, -3, 12, 1, 9, 4, 3, 2, 9, -5, -18, 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"char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "178.2.a.b", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [1], [1], [1], [3], [1], [-4], [1], [-2], [3], [-6], [1], [2], [-4], [3], [1], [3], [-2], [5], [3], [-4], [-6], [-3], [1], [4], [2], [-5], [-4], [0], [3], [5], [1], [-6], [3], [-12], [-2], [-10], [5], [2], [3], [0], [-4], [-1], [-6], [-6], [-3], [12], [1], [9], [4], [3], [2], [9], [-5], [-18], [-4], [5], [0], [12], [3], [-10], [5], [8], [1], [6], [-6], [-4], [3], [-3], [-12], [-6], [-2], [-1], [-10], [4], [5], [24], [2], [-10], [3], [1], [0], [-12], [-4], [9], [-1], [0], [-6], [-1], [-6], [-8], [-3], [5], [12], [15], [1], [17], [9], [12], [4]]}