# Stored data for newform 1620.1.f.d, downloaded from the LMFDB on 19 April 2024.
{"label": "1620.1.f.d", "space_label": "1620.1.f", "level": 1620, "weight": 1, "hecke_orbit": 4, "hecke_orbit_code": 13511142496274004, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 444672445259310962, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [1, 1]], [23, [1, 1]]], "qexp_display": "q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 20, "char_orbit_label": "f", "char_is_real": true, "Nk2": 1620, "analytic_conductor": 0.8084853204654638, "hecke_ring_index": 1, "level_radical": 30, "projective_image": "D3", "projective_image_type": "Dn", "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "artin_degree": 6, "artin_image": "6.1", "field_poly_is_real_cyclotomic": false, "artin_field_label": "3.1.1620.1", "projective_field_label": "3.1.1620.1", "hecke_ring_index_proved": true, "self_twist_type": 1, "is_self_dual": true, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.507", "prec": 17}, "analytic_rank_proved": true, "char_values": [1620, 2, [811, 1541, 1297], [1, 2, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [1459], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.007", "prec": 17}, {"__RealLiteral__": 0, "data": "0.989", "prec": 17}, {"__RealLiteral__": 0, "data": "0.999", "prec": 17}, {"__RealLiteral__": 0, "data": "2.974", "prec": 17}, {"__RealLiteral__": 0, "data": "4.968", "prec": 17}, {"__RealLiteral__": 0, "data": "10.911", "prec": 20}], "related_objects": ["ArtinRepresentation/2.2e2_3e4_5.3t2.2"], "self_twist_discs": [-20], "cm_discs": [-20], "rm_discs": [], "relative_dim": 1, "trace_display": [1, 0, 1, -1], "traces": [0, 1, 1, 0, 1, 1, 0, -1, 1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, -1, -1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 1, -1, 0, 2, 0, 0, -1, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, -1, 0, 0, 2, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 0, 0, -1, 0, -1, 0, 0, -1, 0, 0, -1, -1, 0, 0, 0, 0, 1, -1, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, -1, 0, -1, -1, 0, 1, 0, 0, 2, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, -1, 0, 0, 0, 0, -1, -1, 0, 0, 2, 0, -1, -1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, -1, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, -1, 1, 0, 0, -1, 0, -1, -1, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, -1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 1, 0, 0, 2, -1, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, -1, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, -1, -1, 0, -1, 2, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, -1, -1, 0, 2, -1, 0, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 2, 0, 0, -1, -1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, -1, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, -1, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 1, -1, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, -2, 0, 0, 1, 0, -1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, -1, 0, -1, 1, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 1, 0, 0, 2, 0, 0, -1, 0, 0, 1, -1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, -1, -1, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, -1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 2, 2, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, -1, -1, 0, -1, 2, 0, 0, -1, 0, -1, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, -1, 2, 0, 1, -1, 0, -1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 2, 0, -1, 2, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, -1, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 2, 0, 0, 0, 0, 1, -1, 0, -1, 0, 0, -1, 0, 0, 1, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, -1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, -1, -1, 0, -1, 0, 0, 2, -1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, -1, -1, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 2, 0, 0, 2, 0, 0, -2, 0, 0, 0, -1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 1, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, -2, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, -1, 0, 0, -1, 0, 1, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, -1, 2, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 2, 1, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2, -1, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, -2, -1, 0, 0, -1, 0, 0, 0, 0, -1, -1, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 1, 1, 0, -1, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, -1, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, -1, 1, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, 2, 0, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, -1, 0, 0, 1, -1, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, -1, 0, 0, 0, -1, 0, 2, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 2, -1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, -1, -1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 2, 0, 0, 0, 1, 0, -1, 0, 0, -1, -1, 0, 0, -1, 0, 2, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, -1, -2, 0, 0, -1, 0, 0, 2, 0, 3, 0, 0, 2, 0, 0, 0, -1, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 2, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], "projective_field": [-8, -3, 0, 1], "artin_field": [-8, -3, 0, 1], "weight_parity": -1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 20, 4, -1, 2, -20]], "char_orbit_index": 6, "prim_orbit_index": 4, "embedded_related_objects": [["ArtinRepresentation/2.2e2_3e4_5.3t2.2c1"]], "minimal_twist": "180.1.p.a", "char_is_minimal": true, "conrey_index": 1459, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "sato_tate_group": null, "atkin_lehner_eigenvals": null, "qexp": [[0], [1], [1], [0], [1], [1], [0], [-1], [1], [0], [1], [0], [0], [0], [-1], [0], [1], [0], [0], [0], [1], [0], [0], [-1], [0], [1], [0], [0], [-1], [-1], [0], [0], [1], [0], [0], [-1], [0], [0], [0], [0], [1], [-1], [0], [2], [0], [0], [-1], [-1], [0], [0], [1], [0], [0], [0], [0], [0], [-1], [0], [-1], [0], [0], [-1], [0], [0], [1], [0], [0], [-1], [0], [0], [-1], [0], [0], [0], [0], [0], [0], [0], [0], [0], [1], [0], [-1], [-1], [0], [0], [2], [0], [0], [-1], [0], [0], [-1], [0], [-1], [0], [0], [0], [0], [0], [1]]}