# Stored data for newform 147.2.a.e, downloaded from the LMFDB on 25 April 2024.
{"label": "147.2.a.e", "space_label": "147.2.a", "level": 147, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014398543036563, "dim": 2, "is_polredabs": true, "nf_label": "2.2.8.1", "trace_hash": 1929026430396421515, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-1, 2, 1]], [5, [2, -4, 1]]], "qexp_display": "q+(-1+\\beta )q^{2}+q^{3}+(1-2\\beta )q^{4}+(2+\\cdots)q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 588, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 1.1738009097128217, "hecke_ring_index": 1, "level_radical": 21, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 8, "field_poly_is_real_cyclotomic": true, "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": "0.038", "prec": 17}, "analytic_rank_proved": true, "char_values": [147, 1, [50, 52], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 7], "conrey_indexes": [1], "field_disc": 8, "field_disc_factorization": [[2, 3]], "field_poly": [-2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.015", "prec": 17}, {"__RealLiteral__": 0, "data": "1.936", "prec": 17}, {"__RealLiteral__": 0, "data": "0.171", "prec": 17}, {"__RealLiteral__": 0, "data": "9.134", "prec": 17}, {"__RealLiteral__": 0, "data": "0.932", "prec": 17}, {"__RealLiteral__": 0, "data": "60.645", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [7, 1]], "trace_display": [-2, 2, 4, 0], "traces": [0, 2, -2, 2, 2, 4, -2, 0, -6, 2, 0, -4, 2, 8, 0, 4, 6, 4, -2, 0, -4, 0, 4, -4, -6, 2, -12, 2, 0, -8, 0, -8, 6, -4, -16, 0, 2, -8, -8, 8, -8, 4, 0, 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1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "147.2.a.d", "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, 0], [1, 0], [-1, 1], [1, 0], [1, -2], [2, 1], [-1, 1], [0, 0], [-3, 1], [1, 0], [0, 1], [-2, 0], [1, -2], [4, -1], [0, 0], [2, 1], [3, 0], [2, -3], [-1, 1], [0, -2], [-2, -3], [0, 0], [2, -2], [-2, -4], [-3, 1], [1, 4], [-6, 5], [1, 0], [0, 0], [-4, -2], [0, 1], [-4, 2], [3, 1], [-2, 0], [-8, 5], [0, 0], [1, -2], [-4, 0], [-4, 2], [4, -1], [-4, -1], [2, 3], [0, 0], [0, 4], [-2, 4], [2, 1], [-6, 2], [0, -2], [3, 0], [0, 0], [7, -3], [2, -3], [8, -9], [-2, 0], [-1, 1], [-4, -2], [0, 0], [0, -2], [0, -2], [-4, 2], [-2, -3], [8, 3], [8, -6], [0, 0], [-7, 2], [6, 2], [2, -2], [0, -4], [14, -7], [-2, -4], [0, 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