# Stored data for newform 37.2.a.a, downloaded from the LMFDB on 25 April 2024. {"label": "37.2.a.a", "space_label": "37.2.a", "level": 37, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 33554469, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1127515239490717889, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [2, 1]]], "qexp_display": "q-2q^{2}-3q^{3}+2q^{4}-2q^{5}+6q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 148, "fricke_eigenval": 1, "atkin_lehner_string": "+", "analytic_conductor": 0.2954464874787374, "hecke_ring_index": 1, "level_radical": 37, "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": "0.009", "prec": 17}, "analytic_rank_proved": true, "char_values": [37, 1, [2], [1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [37], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.992", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.946", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.828", "prec": 17}], "related_objects": ["EllipticCurve/Q/37/a"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[37, 1]], "trace_display": [-2, -3, -2, -1], "traces": [0, 1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4, 3, 10, 2, 0, -1, 4, -9, -2, 6, -12, -4, 8, 15, 0, 2, 12, -1, 0, 6, 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true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "37.2.a.a", "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], [-2], [-3], [2], [-2], [6], [-1], [0], [6], [4], [-5], [-6], [-2], [2], [6], [-4], [0], [-12], [0], [-4], [3], [10], [2], [0], [-1], [4], [-9], [-2], [6], [-12], [-4], [8], [15], [0], [2], [12], [-1], [0], [6], [0], [-9], [-6], [2], [-10], [-12], [-4], [-9], [12], [-6], [2], [0], [-4], [1], [18], [10], [0], [0], [-12], [8], [12], [-8], [8], [-6], [-8], [4], [-30], [8], [0], [-6], [-4], [9], [0], [-1], [2], [3], [0], [5], [-12], [4], [8], [9], [18], [-15], [6], [0], [-4], [-18], [0], [4], [24], [2], [4], [12], [18], [0], [-24], [4], [12], [-30], [-2]]}