# Stored data for newform 450.2.e.k, downloaded from the LMFDB on 14 May 2024.
{"label": "450.2.e.k", "space_label": "450.2.e", "level": 450, "weight": 2, "hecke_orbit": 11, "hecke_orbit_code": 45036271185166786, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.1", "trace_hash": 70864368563729515, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [4, 8, 18, -4, 1]], [11, [25, 10, 9, -2, 1]], [17, [-23, -2, 1]]], "qexp_display": "q-\\beta _{2}q^{2}+(-\\beta _{1}+\\beta _{2}+\\beta _{3})q^{3}+(-1+\\cdots)q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "e", "char_is_real": false, "Nk2": 1800, "analytic_conductor": 3.593268090957617, "hecke_ring_index": 1, "level_radical": 30, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.019", "prec": 17}, "analytic_rank_proved": true, "char_values": [450, 3, [101, 127], [2, 3]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [151, 301], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, -2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.856", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "58.980", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1533.658", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c3", "trace_display": [-2, 2, 0, 4], "traces": [0, 4, -2, 2, -2, 0, 2, 4, 4, 2, 0, 2, -4, 0, 4, 0, -2, 4, -4, -12, 0, -16, 2, 4, 2, 0, 0, 20, -8, 12, 0, -8, -2, 10, -2, 0, 2, -32, 6, 0, 0, 2, 8, 10, -4, 0, -8, 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"char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "90.2.i.b", "char_is_minimal": true, "conrey_index": 151, "id": null, "fricke_eigenval": null, "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, 0, 0], [1, 0, 0, 0], [0, 0, -1, 0], [0, -1, 1, 1], [-1, 0, 1, 0], [0, 0, 0, 0], [1, 1, -1, 0], [0, 1, 2, 1], [1, 0, 0, 0], [1, -2, -1, 0], [0, 0, 0, 0], [0, -1, 1, -1], [-1, 0, 0, -1], [0, -1, 0, 2], [2, 1, -2, -2], [0, 0, 0, 0], [0, 0, -1, 0], [1, -4, 0, 2], [-1, 0, 0, 2], [-3, 2, 0, -1], [0, 0, 0, 0], [-4, -3, 0, 2], [1, -1, -1, 2], [2, -2, -2, 4], [0, -1, 1, 1], [0, 0, 0, 0], [0, 2, 0, -1], [5, 0, 0, -1], [-2, -2, 0, 1], [0, 0, 6, 0], [0, 0, 0, 0], [-4, -1, 4, 2], [-1, 0, 1, 0], [1, 0, 3, -2], [0, 2, -1, 2], [0, 0, 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