# Stored data for newform 567.2.f.i, downloaded from the LMFDB on 28 March 2024. {"label": "567.2.f.i", "space_label": "567.2.f", "level": 567, "weight": 2, "hecke_orbit": 9, "hecke_orbit_code": 36029140649902647, "dim": 4, "is_polredabs": true, "nf_label": "4.0.7056.3", "trace_hash": 1277054976997734529, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [49, 0, 7, 0, 1]], [5, [49, 0, 7, 0, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+5\\beta _{2}q^{4}+(\\beta _{1}+\\beta _{3})q^{5}+(1+\\cdots)q^{7}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "f", "char_is_real": false, "Nk2": 2268, "analytic_conductor": 4.527517794606598, "hecke_ring_index": 1, "level_radical": 21, "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": "0.514", "prec": 17}, "analytic_rank_proved": true, "char_values": [567, 3, [407, 325], [1, 3]], "hecke_ring_generator_nbound": 4, "inner_twist_count": 4, "level_primes": [3, 7], "conrey_indexes": [190, 379], "field_disc": 7056, "field_disc_factorization": [[2, 4], [3, 2], [7, 2]], "field_poly": [49, 0, 7, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.942", "prec": 17}, {"__RealLiteral__": 0, "data": "1.050", "prec": 17}, {"__RealLiteral__": 0, "data": "97.117", "prec": 20}, {"__RealLiteral__": 0, "data": "67.815", "prec": 20}, {"__RealLiteral__": 0, "data": "3611.189", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c3", "trace_display": [0, 0, 0, 2], "traces": [0, 4, 0, 0, -10, 0, 0, 2, 0, 0, -28, 0, 0, 4, 0, 0, -22, 0, 0, 28, 0, 0, 14, 0, 0, -4, 0, 0, -20, 0, 0, -6, 0, 0, 0, 0, 0, -12, 0, 0, 42, 0, 0, -16, 0, 0, -84, 0, 0, -2, 0, 0, 20, 0, 0, 28, 0, 0, -28, 0, 0, 16, 0, 0, 52, 0, 0, 4, 0, 0, -14, 0, 0, 0, 0, 0, -70, 0, 0, 8, 0, 0, 28, 0, 0, 0, 0, 0, 42, 0, 0, 8, 0, 0, 0, 0, 0, 24, 0, 0, 40, 0, 0, 26, 0, 0, 0, 0, 0, 36, 0, 0, 22, 0, 0, -42, 0, 0, 0, 0, 0, 8, 0, 0, -30, 0, 0, 24, 0, 0, -28, 0, 0, 14, 0, 0, 0, 0, 0, 24, 0, 0, -42, 0, 0, -56, 0, 0, 30, 0, 0, -4, 0, 0, 28, 0, 0, 28, 0, 0, 70, 0, 0, 40, 0, 0, -84, 0, 0, 18, 0, 0, 160, 0, 0, 4, 0, 0, 98, 0, 0, -56, 0, 0, 126, 0, 0, 0, 0, 0, -196, 0, 0, -4, 0, 0, -10, 0, 0, -12, 0, 0, -56, 0, 0, 14, 0, 0, -88, 0, 0, -44, 0, 0, -28, 0, 0, -12, 0, 0, -70, 0, 0, -14, 0, 0, 56, 0, 0, -40, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, -160, 0, 0, 28, 0, 0, -42, 0, 0, 84, 0, 0, 10, 0, 0, -6, 0, 0, 224, 0, 0, 0, 0, 0, 20, 0, 0, -80, 0, 0, 84, 0, 0, 46, 0, 0, 84, 0, 0, -8, 0, 0, -28, 0, 0, -68, 0, 0, 0, 0, 0, 0, 0, 0, -168, 0, 0, 16, 0, 0, -154, 0, 0, 76, 0, 0, 42, 0, 0, -28, 0, 0, -80, 0, 0, 28, 0, 0, -42, 0, 0, -16, 0, 0, -42, 0, 0, -40, 0, 0, 56, 0, 0, -38, 0, 0, 0, 0, 0, -4, 0, 0, 70, 0, 0, 4, 0, 0, -140, 0, 0, 42, 0, 0, 28, 0, 0, 120, 0, 0, -20, 0, 0, -42, 0, 0, 84, 0, 0, -58, 0, 0, 0, 0, 0, 144, 0, 0, 14, 0, 0, 14, 0, 0, -240, 0, 0, 0, 0, 0, 140, 0, 0, -24, 0, 0, -44, 0, 0, 12, 0, 0, -56, 0, 0, -64, 0, 0, 130, 0, 0, -168, 0, 0, 98, 0, 0, 38, 0, 0, 0, 0, 0, -16, 0, 0, 112, 0, 0, -104, 0, 0, -90, 0, 0, 0, 0, 0, 0, 0, 0, -98, 0, 0, 26, 0, 0, -28, 0, 0, 84, 0, 0, -50, 0, 0, 420, 0, 0, 52, 0, 0, -84, 0, 0, 8, 0, 0, 0, 0, 0, -28, 0, 0, 168, 0, 0, -12, 0, 0, 40, 0, 0, -128, 0, 0, 14, 0, 0, 0, 0, 0, 132, 0, 0, -8, 0, 0, 56, 0, 0, -112, 0, 0, -60, 0, 0, 0, 0, 0, 196, 0, 0, 0, 0, 0, -84, 0, 0, 52, 0, 0, 98, 0, 0, -80, 0, 0, -140, 0, 0, 28, 0, 0, -126, 0, 0, 116, 0, 0, 0, 0, 0, 16, 0, 0, -56, 0, 0, -8, 0, 0, 120, 0, 0, -64, 0, 0, -56, 0, 0, 28, 0, 0, 252, 0, 0, 20, 0, 0, 14, 0, 0, -152, 0, 0, 140, 0, 0, 0, 0, 0, 112, 0, 0, -42, 0, 0, 66, 0, 0, 0, 0, 0, -84, 0, 0, 60, 0, 0, 40, 0, 0, 56, 0, 0, -112, 0, 0, 76, 0, 0, -42, 0, 0, -62, 0, 0, 168, 0, 0, 62, 0, 0, 140, 0, 0, 80, 0, 0, 0, 0, 0, 4, 0, 0, -84, 0, 0, -46, 0, 0, 0, 0, 0, 0, 0, 0, -100, 0, 0, 112, 0, 0, 0, 0, 0, 28, 0, 0, -252, 0, 0, -168, 0, 0, -28, 0, 0, 4, 0, 0, -180, 0, 0, -24, 0, 0, 42, 0, 0, 168, 0, 0, -176, 0, 0, -16, 0, 0, 28, 0, 0, 0, 0, 0, 20, 0, 0, -84, 0, 0, 14, 0, 0, 6, 0, 0, -588, 0, 0, 28, 0, 0, 28, 0, 0, 52, 0, 0, 140, 0, 0, 80, 0, 0, 0, 0, 0, -72, 0, 0, 210, 0, 0, -120, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 16, 0, 0, 56, 0, 0, -136, 0, 0, 294, 0, 0, 18, 0, 0, 168, 0, 0, -28, 0, 0, -20, 0, 0, 24, 0, 0, -168, 0, 0, 42, 0, 0, 44, 0, 0, -8, 0, 0, -56, 0, 0, 64, 0, 0, 30, 0, 0, 0, 0, 0, 168, 0, 0, 42, 0, 0, -168, 0, 0, 140, 0, 0, -42, 0, 0, -112, 0, 0, -140, 0, 0, 60, 0, 0, 0, 0, 0, -112, 0, 0, 52, 0, 0, 28, 0, 0, -168, 0, 0, 2, 0, 0, -220, 0, 0, 16, 0, 0, 0, 0, 0, 56, 0, 0, 168, 0, 0, 26, 0, 0, -210, 0, 0, 140, 0, 0, 30, 0, 0, -8, 0, 0, -588, 0, 0, -20, 0, 0, -154, 0, 0, -64, 0, 0, 42, 0, 0, 12, 0, 0, 140, 0, 0, -28, 0, 0, 84, 0, 0, 0, 0, 0, -84, 0, 0, -4, 0, 0, -56, 0, 0, 84, 0, 0, -200, 0, 0, 128, 0, 0, -98, 0, 0, 12, 0, 0, 280, 0, 0, -14, 0, 0, 168, 0, 0, -48, 0, 0, 0, 0, 0, 42, 0, 0, -224, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 112, 0, 0, 44, 0, 0, -80, 0, 0, 100, 0, 0, -168, 0, 0, 48, 0, 0, 176, 0, 0, -98, 0, 0, 28, 0, 0, -140, 0, 0, 140, 0, 0, 8, 0, 0, 42, 0, 0, 76, 0, 0, 252], "weight_parity": 1, "has_non_self_twist": 1, "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, 3, 2, -1, 2, 0], [1, 1, 9, 3, 1, 3, 0], [1, 1, 9, 4, -1, 6, 0]], "char_orbit_index": 6, "prim_orbit_index": 3, "minimal_twist": "189.2.a.f", "char_is_minimal": false, "conrey_index": 190, "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, 1, 0, 0], [0, 0, 0, 0], [0, 0, 5, 0], [0, 1, 0, 1], [0, 0, 0, 0], [1, 0, 1, 0], [0, 0, 0, 3], [0, 0, 0, 0], [-7, 0, 0, 0], [0, -1, 0, 0], [0, 0, 0, 0], [0, 0, -2, 0], [0, 1, 0, 1], [0, 0, 0, 0], [-11, 0, -11, 0], [0, 0, 0, 0], [0, 0, 0, 0], [7, 0, 0, 0], [0, -5, 0, 0], [0, 0, 0, 0], [0, 0, -7, 0], [0, 3, 0, 3], [0, 0, 0, 0], [-2, 0, -2, 0], [0, 0, 0, -2], [0, 0, 0, 0], [-5, 0, 0, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, 3, 0], [0, -5, 0, -5], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0], [-3, 0, 0, 0], [0, 7, 0, 0], [0, 0, 0, 0], [0, 0, -21, 0], [0, -1, 0, -1], [0, 0, 0, 0], [-8, 0, -8, 0], [0, 0, 0, -5], [0, 0, 0, 0], [-21, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, -2, 0, -2], [0, 0, 0, 0], [10, 0, 10, 0], [0, 0, 0, 0], [0, 0, 0, 0], [7, 0, 0, 0], [0, -3, 0, 0], [0, 0, 0, 0], [0, 0, 14, 0], [0, 0, 0, 0], [0, 0, 0, 0], [8, 0, 8, 0], [0, 0, 0, 3], [0, 0, 0, 0], [13, 0, 0, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, -2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-7, 0, -7, 0], [0, 0, 0, 3], [0, 0, 0, 0], [0, 0, 0, 0], [0, -3, 0, 0], [0, 0, 0, 0], [0, 0, 35, 0], [0, -1, 0, -1], [0, 0, 0, 0], [4, 0, 4, 0], [0, 0, 0, -11], [0, 0, 0, 0], [7, 0, 0, 0], [0, 6, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -8, 0, -8], [0, 0, 0, 0], [21, 0, 21, 0], [0, 0, 0, -7], [0, 0, 0, 0], [2, 0, 0, 0], [0, -15, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 7, 0, 7], [0, 0, 0, 0], [12, 0, 12, 0], [0, 0, 0, 1], [0, 0, 0, 0], [10, 0, 0, 0]]}