# Stored data for newform 405.2.a.j, downloaded from the LMFDB on 24 April 2024. {"label": "405.2.a.j", "space_label": "405.2.a", "level": 405, "weight": 2, "hecke_orbit": 10, "hecke_orbit_code": 40532396679889301, "dim": 3, "is_polredabs": true, "nf_label": "3.3.564.1", "trace_hash": 2275373870602684034, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [3, -5, -1, 1]], [11, [-12, -8, 2, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+(2+\\beta _{2})q^{4}+q^{5}+(2-\\beta _{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": 1620, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 3.2339412818618554, "hecke_ring_index": 1, "level_radical": 15, "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": "0.008", "prec": 17}, "analytic_rank_proved": true, "char_values": [405, 1, [326, 82], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 5], "conrey_indexes": [1], "field_disc": 564, "field_disc_factorization": [[2, 2], [3, 1], [47, 1]], "field_poly": [3, -5, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.047", "prec": 17}, {"__RealLiteral__": 0, "data": "2.896", "prec": 17}, {"__RealLiteral__": 0, "data": "0.750", "prec": 17}, {"__RealLiteral__": 0, "data": "21.659", "prec": 20}, {"__RealLiteral__": 0, "data": "9.991", "prec": 17}, {"__RealLiteral__": 0, "data": "235.415", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, 1], [5, -1]], "trace_display": [1, 0, 3, 5], "traces": [0, 3, 1, 0, 5, 3, 0, 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"char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "45.2.e.b", "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, 0], [1, 0, 0], [0, 1, 0], [0, 0, 0], [2, 0, 1], [1, 0, 0], [0, 0, 0], [2, -1, 0], [1, 1, 1], [0, 0, 0], [0, 1, 0], [-1, 0, -1], [0, 0, 0], [1, 0, -1], [-4, 2, -1], [0, 0, 0], [1, 2, 0], [-1, 0, -1], [0, 0, 0], [1, 0, -1], [2, 0, 1], [0, 0, 0], [-1, -2, -1], [2, -1, 2], [0, 0, 0], [1, 0, 0], [-1, 0, -1], [0, 0, 0], [3, -3, 1], [-1, -2, 2], [0, 0, 0], [1, 4, -1], [6, -1, 0], [0, 0, 0], [-1, -2, -1], [2, -1, 0], [0, 0, 0], [3, -2, 1], [-1, 0, -1], [0, 0, 0], [1, 1, 1], [-4, -2, -1], [0, 0, 0], [3, 2, 1], [-7, -2, -1], [0, 0, 0], [-2, 4, 1], [5, -3, -1], [0, 0, 0], [1, -4, 1], [0, 1, 0], [0, 0, 0], [-3, -2, 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