# Stored data for newform 380.2.k.a, downloaded from the LMFDB on 25 April 2024. {"label": "380.2.k.a", "space_label": "380.2.k", "level": 380, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 687228322172, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 2044417823612894094, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [2, 2, 1]]], "qexp_display": "q+(-1+i)q^{2}+(-1-i)q^{3}-2iq^{4}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 20, "char_orbit_label": "k", "char_is_real": false, "Nk2": 1520, "analytic_conductor": 3.0343152768086545, "hecke_ring_index": 1, "level_radical": 190, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.270", "prec": 17}, "analytic_rank_proved": true, "char_values": [380, 4, [191, 77, 21], [2, 1, 4]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 5, 19], "conrey_indexes": [267, 343], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.045", "prec": 17}, {"__RealLiteral__": 0, "data": "1.911", "prec": 17}, {"__RealLiteral__": 0, "data": "0.304", "prec": 17}, {"__RealLiteral__": 0, "data": "10.771", "prec": 20}, {"__RealLiteral__": 0, "data": "2.852", "prec": 17}, {"__RealLiteral__": 0, "data": "84.747", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c4", "trace_display": [-2, -2, -4, -4], "traces": [0, 2, -2, -2, 0, -4, 4, -4, 4, 0, 6, 0, -4, 0, 0, 2, -8, 10, 2, -2, -4, 8, 0, 8, 0, 6, 0, -8, 8, 0, -8, 0, 8, 0, -20, 12, -4, 0, 2, 0, -4, 4, -8, -12, 0, -2, -16, -4, 8, 0, -14, 0, 0, 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"atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [-1, 1], [-1, -1], [0, -2], [-2, -1], [2, 0], [-2, 2], [2, 2], [0, -1], [3, -1], [0, 0], [-2, 2], [0, 0], [0, -4], [1, 3], [-4, 0], [5, 5], [1, 1], [-1, 0], [-2, 4], [4, 0], [0, 0], [4, 4], [0, -4], [3, 4], [0, 0], [-4, 4], [4, 4], [0, 6], [-4, -2], [0, 0], [4, -4], [0, 0], [-10, 0], [6, -2], [-2, 0], [0, 0], [1, -1], [0, 0], [-2, -6], [2, 0], [-4, 4], [-6, -6], [0, 0], [-1, 2], [-8, 0], [-2, 2], [4, 4], [0, -1], [-7, -1], [0, -10], [0, 0], [-10, 10], [0, -8], [0, 0], [-8, 0], [1, 1], [-6, -6], [10, 0], [6, -2], [2, 0], [0, 0], [2, 2], [0, 8], [0, 0], [0, 0], [3, -3], [10, -10], [0, -8], [-4, 8], [0, 0], [2, -2], [5, -5], [0, 0], [1, -7], [0, 2], [0, 0], [0, 0], 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