# Stored data for newform 78.2.a.a, downloaded from the LMFDB on 25 April 2024.
{"label": "78.2.a.a", "space_label": "78.2.a", "level": 78, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 33554510, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 124393021660496081, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q-q^{2}-q^{3}+q^{4}+2q^{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": 312, "fricke_eigenval": -1, "atkin_lehner_string": "++-", "analytic_conductor": 0.622833135765987, "hecke_ring_index": 1, "level_radical": 78, "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": "0.022", "prec": 17}, "analytic_rank_proved": true, "char_values": [78, 1, [53, 67], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 13], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.022", "prec": 17}, {"__RealLiteral__": 0, "data": "0.997", "prec": 17}, {"__RealLiteral__": 0, "data": "0.055", "prec": 17}, {"__RealLiteral__": 0, "data": "1.999", "prec": 17}, {"__RealLiteral__": 0, "data": "0.186", "prec": 17}, {"__RealLiteral__": 0, "data": "4.959", "prec": 17}], "related_objects": ["EllipticCurve/Q/78/a"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [3, 1], [13, -1]], "trace_display": [-1, -1, 2, 4], "traces": [0, 1, -1, -1, 1, 2, 1, 4, -1, 1, -2, -4, -1, 1, -4, -2, 1, 2, -1, -8, 2, -4, 4, 0, 1, -1, -1, -1, 4, 6, 2, -4, -1, 4, -2, 8, 1, -2, 8, -1, -2, -10, 4, 4, -4, 2, 0, 8, -1, 9, 1, -2, 1, -10, 1, -8, 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"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], [2], [1], [4], [-1], [1], [-2], [-4], [-1], [1], [-4], [-2], [1], [2], [-1], [-8], [2], [-4], [4], [0], [1], [-1], [-1], [-1], [4], [6], [2], [-4], [-1], [4], [-2], [8], [1], [-2], [8], [-1], [-2], [-10], [4], [4], [-4], [2], [0], [8], [-1], [9], [1], [-2], [1], [-10], [1], [-8], [-4], [8], [-6], [4], [-2], [-2], [4], [4], [1], [2], [-4], [-16], [2], [0], [-8], [-8], [-1], [2], [2], [1], [-8], [-16], [1], [8], [2], [1], [10], [12], [-4], [4], [-4], [-6], [4], [14], [-2], [4], [0], [4], [-8], [-16], [1], [10], [-9], [-4], [-1]]}