# Stored data for newform 363.2.a.e, downloaded from the LMFDB on 25 April 2024.
{"label": "363.2.a.e", "space_label": "363.2.a", "level": 363, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014398543036779, "dim": 2, "is_polredabs": true, "nf_label": "2.2.5.1", "trace_hash": 1480375511116051357, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-1, 1, 1]]], "qexp_display": "q-\\beta q^{2}+q^{3}+(-1+\\beta )q^{4}+(-2+\\beta )q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1452, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 2.898569593372478, "hecke_ring_index": 1, "level_radical": 33, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 10, "field_poly_is_real_cyclotomic": true, "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": "0.011", "prec": 17}, "analytic_rank_proved": true, "char_values": [363, 1, [122, 244], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 11], "conrey_indexes": [1], "field_disc": 5, "field_disc_factorization": [[5, 1]], "field_poly": [-1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.986", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.663", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "65.309", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [11, -1]], "trace_display": [-1, 2, -3, -6], "traces": [0, 2, -1, 2, -1, -3, -1, -6, 0, 2, -1, 0, -1, -8, 3, -3, -3, -1, -1, -5, 4, -6, 0, -2, 0, -3, 9, 2, 3, 0, -1, -1, 9, 0, -2, 9, -1, -4, -5, -8, 5, 6, 3, -8, 0, -3, 11, 1, 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"minimal_twist": "33.2.e.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, 0], [1, 0], [0, -1], [1, 0], [-1, 1], [-2, 1], [0, -1], [-3, 0], [-1, 2], [1, 0], [-1, 1], [0, 0], [-1, 1], [-3, -2], [0, 3], [-2, 1], [0, -3], [-1, 1], [0, -1], [-4, 3], [3, -2], [-3, 0], [0, 0], [1, -4], [-1, 2], [0, -3], [2, 5], [1, 0], [3, -3], [-2, 4], [-1, 1], [1, -3], [5, -1], [0, 0], [-1, 0], [6, -3], [-1, 1], [-1, -2], [-3, 1], [-3, -2], [4, -3], [7, -8], [0, 3], [-5, 2], [0, 0], [-2, 1], [4, 3], [1, -1], [0, -3], [2, 0], [3, 3], [-1, 1], [1, -3], [-9, 1], [0, -1], [0, 0], [3, -6], [-4, 3], [-4, -2], [6, -7], [3, -2], [-6, 3], [3, 2], [-3, 0], [1, 2], [4, -1], [0, 0], [-4, 9], [2, -1], [1, -4], [3, -3], [0, 9], [-1, 2], [2, -2], [2, 3], [0, -3], [7, -4], [0, 0], [2, 5], [-7, 4], [-3, 3], [1, 0], [8, 1], [3, 6], [3, -3], [3, -2], [-2, 3], [-2, 4], [0, 0], [3, 4], [-1, 1], [9, 6], [-5, 1], [1, -3], [1, 0], [11, -7], [5, -1], [-6, 13], [0, -2], [0, 0], [-3, 0]]}