# Stored data for newform 370.2.a.f, downloaded from the LMFDB on 19 April 2024.
{"label": "370.2.a.f", "space_label": "370.2.a", "level": 370, "weight": 2, "hecke_orbit": 6, "hecke_orbit_code": 22517998170407282, "dim": 2, "is_polredabs": true, "nf_label": "2.2.33.1", "trace_hash": 62673602914054360, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [-2, 1]], [7, [-6, 3, 1]]], "qexp_display": "q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}+(-1+\\cdots)q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1480, "fricke_eigenval": -1, "atkin_lehner_string": "---", "analytic_conductor": 2.9544648747873743, "hecke_ring_index": 1, "level_radical": 370, "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": "0.013", "prec": 17}, "analytic_rank_proved": true, "char_values": [370, 1, [297, 261], [1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 1, "level_primes": [2, 5, 37], "conrey_indexes": [1], "field_disc": 33, "field_disc_factorization": [[3, 1], [11, 1]], "field_poly": [-8, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.876", "prec": 17}, {"__RealLiteral__": 0, "data": "0.034", "prec": 17}, {"__RealLiteral__": 0, "data": "9.043", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "61.797", "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], [5, -1], [37, -1]], "trace_display": [2, 4, 2, -3], "traces": [0, 2, 2, 4, 2, 2, 4, -3, 2, 2, 2, -1, 4, 2, -3, 4, 2, -5, 2, -4, 2, -6, -1, 2, 4, 2, 2, -8, -3, -1, 4, -11, 2, -2, -5, 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"level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "370.2.a.f", "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], [2, 0], [1, 0], [1, 0], [2, 0], [-1, -1], [1, 0], [1, 0], [1, 0], [-1, 1], [2, 0], [0, 2], [-1, -1], [2, 0], [1, 0], [-3, 1], [1, 0], [-2, 0], [1, 0], [-2, -2], [-1, 1], [2, -2], [2, 0], [1, 0], [0, 2], [-4, 0], [-1, -1], [1, -3], [2, 0], [-5, -1], [1, 0], [-2, 2], [-3, 1], [-1, -1], [1, 0], [1, 0], [-2, 0], [0, 4], [1, 0], [3, -1], [-2, -2], [5, -1], [-1, 1], [1, 0], [2, -2], [-4, 2], [2, 0], [2, 3], [1, 0], [-6, 2], [0, 2], [-1, -1], [-4, 0], [-1, 1], [-1, -1], [-4, 0], [1, -3], [8, -2], [2, 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