# Stored data for newform 512.2.a.f, downloaded from the LMFDB on 20 April 2024.
{"label": "512.2.a.f", "space_label": "512.2.a", "level": 512, "weight": 2, "hecke_orbit": 6, "hecke_orbit_code": 22517998170407424, "dim": 2, "is_polredabs": true, "nf_label": "2.2.8.1", "trace_hash": 906415289250718537, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [2, -4, 1]], [5, [0, 1]], [7, [0, 1]]], "qexp_display": "q+(2+\\beta )q^{3}+(3+4\\beta )q^{9}+(2-3\\beta )q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2048, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 4.088340583489556, "hecke_ring_index": 1, "level_radical": 2, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 8, "field_poly_is_real_cyclotomic": true, "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": "0.631", "prec": 17}, "analytic_rank_proved": true, "char_values": [512, 1, [511, 5], [1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2], "conrey_indexes": [1], "field_disc": 8, "field_disc_factorization": [[2, 3]], "field_poly": [-2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.045", "prec": 17}, {"__RealLiteral__": 0, "data": "1.903", "prec": 17}, {"__RealLiteral__": 0, "data": "0.196", "prec": 17}, {"__RealLiteral__": 0, "data": "16.098", "prec": 20}, {"__RealLiteral__": 0, "data": "0.996", "prec": 17}, {"__RealLiteral__": 0, "data": "167.525", "prec": 24}], "related_objects": [], "self_twist_discs": [-8], "cm_discs": [-8], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.1.d1", "atkin_lehner_eigenvals": [[2, -1]], "trace_display": [0, 4, 0, 0], "traces": [0, 2, 0, 4, 0, 0, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, -10, 0, 16, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -12, 0, 12, 0, 0, 0, 0, 0, -14, 0, -16, 0, 0, 0, 0, 0, 20, 0, -20, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 46, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 22, 0, -24, 0, 0, 0, 0, 0, 4, 0, -20, 0, 0, 0, 0, 0, 12, 0, 12, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, -26, 0, 20, 0, 0, 0, 0, 0, -28, 0, -28, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, 36, 0, 36, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, -30, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92, 0, 0, 0, 0, 0, 44, 0, 44, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 30, 0, 48, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, -68, 0, 16, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 28, 0, -72, 0, 0, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, 38, 0, -4, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, -76, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44, 0, 24, 0, 0, 0, 0, 0, 68, 0, -52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -42, 0, 4, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 52, 0, -128, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 84, 0, -60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 76, 0, -20, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 12, 0, 36, 0, 0, 0, 0, 0, -46, 0, -12, 0, 0, 0, 0, 0, -20, 0, -28, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, -52, 0, 0, 0, 0, 0, -84, 0, -60, 0, 0, 0, 0, 0, -68, 0, 48, 0, 0, 0, 0, 0, 0, 0, 68, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 148, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 50, 0, -8, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, -76, 0, 0, 0, 0, 0, 0, 0, -192, 0, 68, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, -52, 0, 44, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 138, 0, 80, 0, 0, 0, 0, 0, -60, 0, -60, 0, 0, 0, 0, 0, 0, 0, 156, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, -108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 144, 0, 0, 0, 0, 0, -12, 0, -60, 0, 0, 0, 0, 0, 92, 0, 0, 0, 0, 0, 0, 0, 20, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -58, 0, 80, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 108, 0, 12, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, -36, 0, -84, 0, 0, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, -100, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, -62, 0, -132, 0, 0, 0, 0, 0, -64, 0, 44, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 124, 0, 0, 0, 0, 0, 0, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 4, -1, 2, -8]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "512.2.a.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, 0], [2, 1], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [3, 4], [0, 0], [2, -3], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -4], [0, 0], [6, -1], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-5, 0], [0, 0], [8, 8], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-2, -4], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-6, 0], [0, 0], [6, -5], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-7, 0], [0, 0], [-8, -8], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [10, 4], [0, 0], [-10, 3], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [6, 7], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -12], [0, 0], [-10, -5], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [23, 12], [0, 0], [2, 9], [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, 12], [0, 0], [-18, -1], [0, 0]]}