# Stored data for newform 138.2.a.d, downloaded from the LMFDB on 23 April 2024.
{"label": "138.2.a.d", "space_label": "138.2.a", "level": 138, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13510798915666058, "dim": 2, "is_polredabs": true, "nf_label": "2.2.5.1", "trace_hash": 1791926230091472914, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [-4, 2, 1]]], "qexp_display": "q+q^{2}+q^{3}+q^{4}+(-1+\\beta )q^{5}+q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 552, "fricke_eigenval": -1, "atkin_lehner_string": "---", "analytic_conductor": 1.1019355478936692, "hecke_ring_index": 2, "level_radical": 138, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 10, "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": "0.019", "prec": 17}, "analytic_rank_proved": true, "char_values": [138, 1, [47, 97], [1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [2, 3, 23], "conrey_indexes": [1], "field_disc": 5, "field_disc_factorization": [[5, 1]], "field_poly": [-1, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.020", "prec": 17}, {"__RealLiteral__": 0, "data": "1.951", "prec": 17}, {"__RealLiteral__": 0, "data": "0.168", "prec": 17}, {"__RealLiteral__": 0, "data": "9.109", "prec": 17}, {"__RealLiteral__": 0, "data": "1.393", "prec": 17}, {"__RealLiteral__": 0, "data": "59.828", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, -1], [23, -1]], "trace_display": [2, 2, -2, 0], "traces": [0, 2, 2, 2, 2, -2, 2, 0, 2, 2, -2, -6, 2, 0, 0, -2, 2, -8, 2, -2, -2, 0, -6, 2, 2, 2, 0, 2, 0, 0, -2, 4, 2, -6, -8, -20, 2, 18, -2, 0, -2, -4, 0, -14, -6, 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"char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "138.2.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, 0], [1, 0], [1, 0], [-1, 1], [1, 0], [0, -2], [1, 0], [1, 0], [-1, 1], [-3, -1], [1, 0], [0, 2], [0, -2], [-1, 1], [1, 0], [-4, 0], [1, 0], [-1, 3], [-1, 1], [0, -2], [-3, -1], [1, 0], [1, 0], [1, -2], [0, 2], [1, 0], [0, -2], [0, -2], [-1, 1], [2, -2], [1, 0], [-3, -1], [-4, 0], [-10, 2], [1, 0], [9, 1], [-1, 3], [0, 2], [-1, 1], [-2, 0], [0, -2], [-7, 1], [-3, -1], [-1, 1], [1, 0], [4, 0], [1, 0], [13, 0], [1, -2], [-4, 0], [0, 2], [3, 1], [1, 0], [-2, -2], [0, -2], [-1, 3], [0, -2], [0, -4], [-1, 1], [3, -1], [2, -2], [0, -2], [1, 0], [10, -2], [-3, -1], [3, 3], [-4, 0], [1, 0], [-10, 2], [0, 4], [1, 0], [0, -2], [9, 1], [1, -2], [-1, 3], [10, 6], [0, 2], [0, 2], [-1, 1], [1, 0], [-2, 0], [11, 1], [0, -2], [4, -4], [-7, 1], [0, -2], [-3, -1], [-6, -2], [-1, 1], [-20, 0], [1, 0], [2, -2], [4, 0], [16, -4], [1, 0], [-4, 2], [13, 0], [-3, -1], [1, -2]]}