# Stored data for newform 164.1.d.b, downloaded from the LMFDB on 25 April 2025.
{"Nk2": 164, "analytic_conductor": 0.08184666207181239, "analytic_rank": 0, "analytic_rank_proved": true, "artin_degree": 16, "artin_field": [1, 2, -1, -2, 0, 0, 3, 0, 1], "artin_field_label": "8.0.17643776.1", "artin_image": "16.7", "char_conductor": 164, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 4, "char_orbit_label": "d", "char_order": 2, "char_parity": -1, "char_values": [164, 2, [83, 129], [1, 1]], "cm_discs": [-164], "conrey_index": 163, "dim": 2, "embedded_related_objects": [["ArtinRepresentation/2.2e2_41.8t6.2c1"], ["ArtinRepresentation/2.2e2_41.8t6.2c2"]], "field_disc": 8, "field_disc_factorization": [[2, 3]], "field_poly": [-2, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": true, "field_poly_root_of_unity": 8, "has_non_self_twist": 1, "hecke_cutters": [[3, [-2, 0, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503805802578084, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 164, 4, -1, 2, -164], [1, 1, 4, 2, -1, 2, 0], [1, 1, 41, 2, 1, 2, 0]], "is_cm": true, "is_largest": true, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": true, "is_twist_minimal": true, "label": "164.1.d.b", "level": 164, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 41], "level_radical": 82, "minimal_twist": "164.1.d.b", "nf_label": "2.2.8.1", "prim_orbit_index": 4, "projective_field": [-4, 0, -5, 0, 1], "projective_field_label": "4.2.6724.1", "projective_image": "D4", "projective_image_type": "Dn", "qexp_display": "q-q^{2}-\\beta q^{3}+q^{4}+\\beta q^{6}+\\beta q^{7}-q^{8}+\\cdots", "related_objects": ["ArtinRepresentation/2.2e2_41.8t6.2"], "relative_dim": 2, "rm_discs": [], "self_twist_discs": [-164], "self_twist_type": 1, "space_label": "164.1.d", "trace_display": [-2, 0, 0, 0], "trace_hash": 320379962415646211, "trace_moments": [{"__RealLiteral__": 0, "data": "-0.016", "prec": 20}, {"__RealLiteral__": 0, "data": "1.907", "prec": 17}, {"__RealLiteral__": 0, "data": "-0.249", "prec": 20}, {"__RealLiteral__": 0, "data": "30.412", "prec": 20}, {"__RealLiteral__": 0, "data": "-3.984", "prec": 20}, {"__RealLiteral__": 0, "data": "486.226", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.879", "prec": 17}, "traces": [0, 2, -2, 0, 2, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, -4, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, -2, -2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, -2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 2, 0, 0, -4, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 2, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, -4, -2, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, -2, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], "weight": 1, "weight_parity": -1, "id": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "fricke_eigenval": null, "sato_tate_group": null, "qexp": [[0, 0], [1, 0], [-1, 0], [0, -1], [1, 0], [0, 0], [0, 1], [0, 1], [-1, 0], [1, 0], [0, 0], [0, 1], [0, -1], [0, 0], [0, -1], [0, 0], [1, 0], [0, 0], [-1, 0], [0, -1], [0, 0], [-2, 0], [0, -1], [0, 0], [0, 1], [-1, 0], [0, 0], [0, 0], [0, 1], [0, 0], [0, 0], [0, 0], [-1, 0], [-2, 0], [0, 0], [0, 0], [1, 0], [0, 0], [0, 1], [0, 0], [0, 0], [1, 0], [2, 0], [0, 0], [0, 1], [0, 0], [0, 0], [0, -1], [0, -1], [1, 0], [1, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -1], [2, 0], [0, 0], [0, 0], [0, 0], [-2, 0], [0, 0], [0, 1], [1, 0], [0, 0], [2, 0], [0, 1], [0, 0], [0, 0], [0, 0], [0, -1], [-1, 0], [0, 0], [0, 0], [0, 1], [0, -1], [2, 0], [0, 0], [0, -1], [0, 0], [-1, 0], [-1, 0], [0, 0], [-2, 0], [0, 0], [0, 0], [0, 0], [0, -1], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 1], [0, 0], [0, 1], [0, 0], [-1, 0], [0, 1], [-1, 0]]}