# Stored data for newform 224.2.u.a, downloaded from the LMFDB on 16 January 2026.
{"Nk2": 896, "analytic_conductor": 1.7886490052766806, "analytic_rank": 1, "analytic_rank_proved": true, "char_conductor": 32, "char_degree": 4, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 21, "char_orbit_label": "u", "char_order": 8, "char_parity": 1, "char_values": [224, 8, [127, 197, 129], [8, 3, 8]], "cm_discs": [], "conrey_index": 29, "dim": 4, "field_disc": 256, "field_disc_factorization": [[2, 8]], "field_poly": [1, 0, 0, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 8, "has_non_self_twist": 1, "hecke_cutters": [[3, [8, 16, 12, 4, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 1374423089376, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 32, 7, 1, 8, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "224.2.u.a", "level": 224, "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, 7], "level_radical": 14, "minimal_twist": "224.2.u.a", "nf_label": "4.0.256.1", "prim_orbit_index": 7, "qexp_display": "q+(-1+\\zeta_{8}^{2})q^{2}+(-1-\\zeta_{8}-\\zeta_{8}^{2}+\\cdots)q^{3}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c8", "self_twist_discs": [], "self_twist_type": 0, "space_label": "224.2.u", "trace_display": [-4, -4, -8, 0], "trace_hash": 1953048782465253633, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.766", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "43.489", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "754.019", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.152", "prec": 17}, "traces": [0, 4, -4, -4, 0, -8, 8, 0, 8, -8, 8, -12, -8, 0, 0, 0, -16, 0, 0, -4, 0, 4, 4, -4, 0, 16, 8, 8, 0, -16, -16, -24, 16, 40, 0, 0, 16, -16, 16, 0, -16, -8, 0, -16, 16, 24, 0, 0, 16, 0, -32, 0, -16, 20, 0, 40, 0, 8, 28, -20, 32, -16, 24, -4, 0, 0, -40, 16, 0, 8, 8, 0, -32, 24, 4, 12, -24, -8, 0, 0, 32, 0, 0, -4, -8, 0, 12, -24, -40, -32, -8, 0, 8, 24, -24, 16, -32, 16, -4, -4, 32, -8, 0, -24, 16, -16, -28, 16, -16, -20, 0, 0, 0, 0, -16, 8, -24, 8, 0, 0, -32, -28, 16, 24, 0, -32, 4, -8, -32, 40, 0, 4, 0, -4, -36, 0, 0, 4, -8, -4, -16, 40, 0, 0, 32, 0, 0, 4, 24, -20, 32, -12, 16, 0, -4, 64, 0, 24, 0, -24, -32, 0, -12, 28, 16, -112, 32, 40, 16, -16, 0, 20, 8, 0, 0, 0, 48, 0, 64, -28, -32, -16, -8, 0, -16, 8, -64, 0, 48, -8, -16, -16, 32, 0, -16, 0, 8, 8, 52, 32, 0, 40, 8, 16, 0, 32, 48, 0, 0, 0, 0, -8, 16, -24, -36, 40, 32, -8, 20, -32, -80, 0, -8, -48, 0, -76, 64, -44, 16, 32, 0, 16, -8, 4, -24, 16, 40, -56, 0, 0, 0, 0, 56, 52, 0, 0, -32, -32, -48, 8, 48, -12, 0, 4, 8, 0, 64, -56, -40, 12, 0, 68, -16, -16, 80, -24, -8, 16, 40, -40, 0, 0, 0, 0, 0, -104, 0, -8, 24, 56, 16, -28, -16, 12, 0, -16, -48, -8, 0, 68, -48, -16, -48, 48, 0, 0, -56, -48, 28, 8, -88, -4, 0, 0, 16, 0, 0, -60, 24, -24, -80, 32, 0, -48, 0, 24, 0, -8, 24, 144, 0, 8, 0, 0, 24, 32, -28, 40, -32, -8, 144, 12, -56, 24, -80, 0, -16, 0, 0, -72, 0, 64, -32, 0, -40, -16, 24, 0, 48, 32, -12, -32, -16, 8, 0, 0, -64, 0, 36, -20, 80, -56, -8, -60, 16, -16, 0, 0, 16, 0, -16, -8, 80, 72, 0, -32, -48, 8, 0, -12, 0, 8, 16, -40, 0, 32, 0, 8, 0, 0, -32, 0, -8, 24, -60, -56, -96, 16, -64, 0, -64, 0, 0, -16, 0, 16, -4, 92, 0, 80, -16, -88, -48, 20, 16, 16, -32, -32, -56, -12, 32, 52, 4, -56, 24, 0, 0, 16, 40, 32, 0, 0, -32, 0, 16, 160, 0, 16, 16, -72, 160, -8, 0, 20, 16, 64, 48, 24, 0, -32, 76, -16, -128, 24, 88, -16, 0, 32, 0, 0, -16, 0, -32, 0, 64, 0, 0, 36, 32, -16, 48, -48, -80, -4, 56, 20, 0, -36, 24, -72, 64, 48, -16, 0, -56, -16, -64, -60, -32, 0, 8, 40, 16, 0, 0, 0, 96, 0, -16, 44, -32, -24, -32, 32, -8, 16, 16, 52, 0, -32, 0, -16, -64, -64, 56, 48, 0, -88, 4, 0, 0, -16, -76, -4, 24, 44, 32, 0, -160, 0, 0, 20, 24, 0, -64, 8, -8, 56, 56, -8, 0, 28, 80, 80, 0, 80, 16, 4, -8, 32, 84, 40, 16, 28, -36, 64, -40, 44, 0, 0, 0, 0, 56, 12, -48, -8, -56, -8, 0, 0, 0, -40, 96, 16, 8, -32, -64, -40, -68, 0, 96, -4, 16, -60, 96, 16, -16, -76, -8, 8, 0, 0, 64, 0, 0, 0, -16, -40, -16, -32, 112, -40, -12, -92, 24, 56, -16, -128, -64, -56, 0, 32, 0, -36, 40, -64, -40, 40, -48, -28, 32, 0, 0, 0, 0, 0, 96, -8, -48, 0, -40, -64, 0, 16, -20, -80, 0, 8, -144, 24, 64, 0, -8, -12, 0, -96, 0, 16, -24, 120, -24, -24, 0, -4, -80, 0, 32, 0, 0, -48, -64, -56, 12, 0, 48, -16, 20, 28, 80, 48, 80, 96, 0, 0, -80, 40, 32, 88, 8, -8, 0, -88, 24, -40, 24, -168, 0, 0, 64, 0, 32, 28, -48, 4, 12, -32, -96, 0, 0, 8, 24, -44, 32, 104, -64, -160, -8, 0, 0, -52, -48, 28, 0, 24, 0, -16, -16, -24, 40, 0, -96, 0, 0, 128, 48, 32, -56, -8, -16, -80, -32, 0, 0, -72, 16, -16, 0, -176, 40, -28, 16, 16, 28, 28, -32, 24, -60, 36, 0, -20, 0, 0, 0, 0, -16, 24, 16, 28, 92, -40, 32, -24, 80, -20, 0, 0, 40, 80, -64, 48, -32, 56, 0, 8, 36, -120, 32, -32, -68, 8, 64, 48, 0, 0, 0, 0, 0, 4, 104, -32, 0, 4, 88, 32, -64, 16, 64, -16, 16, 0, 128, 112, 112, -72, -80, 8, -16, 80, -16, 0, 24, 4, -24, -32, 0, 0, 0, 0, -160, -16, -32, -8, 168, -16, 0, 208, 0, 4, -32, -16, -16, 104, 64, 0, 32, -80, 112, -48, 0, 120, -64, -68, -60, 32, 8, 72, 112, 0, -80, 0, 0, 4, 48, -128, -16, -16, -8, -56, 16, 60, -80, 8, 64, 0, 0, 0, -16, -68, -16, 140, -112, 8, -40, -24, -24, 32, 32, 24, 0, 0, -160, 0, 16, -32, 0, 80, -52, 112, -16, 48, -96, -64, 0, 40, -24, 112, 0, 0, 32, 88, 0, 0, 72, 8, 128, 80, -24, -4, -88, 24, 32, 0, -32, 0, 0, 64, -64, -4, 0, -64, 32, 120, -48, 0, 32, -76, -16, 120, -112, 32, 160, 12, -8, -128, -104, 0, -16, 24, -4, 40, -128, -64, 0, 0, 80, 0, 8, 56, 0, -80, 8, 56, 0, 44, 20, -8, -48, -144, 72, 80, -128, 52, -48, -56, 32, -8, -8, 52, 0, 0, 0, -44, 24, 20, 120, 0, 64, 0, 0, 128, -16, 40, -20, -8, 32, -120, 0, 40, 64, 12, -192, 48, -96, -72, 24, -64, 16, -8, -68, 48, -32], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [-1, 0, 1, 0], [-1, -1, -1, -1], [0, 0, -2, 0], [-2, -2, 0, 0], [2, 2, 0, 0], [0, 1, 0, 0], [2, 0, 2, 0], [-2, 0, 2, 1], [2, 2, -2, -2], [-3, 3, 2, 2], [-2, -2, 2, 2], [0, 2, -2, 0], [0, -1, 0, 1], [0, 4, 4, 4], [-4, 0, 0, 0], [0, 0, 0, 0], [0, -1, -4, -1], [-1, 3, -3, 1], [0, 0, 4, 4], [1, -1, -1, -1], [1, -5, -5, 1], [-1, 0, 1, 0], [0, 0, -4, -4], [4, 3, 4, 0], [2, -2, 2, 2], [2, 2, -2, 2], [0, 0, 0, -2], [-4, -3, -3, -4], [-4, -8, -4, 0], [-6, -2, 0, 2], [4, 0, -4, 0], [10, 4, 0, -4], [0, 0, 0, 0], [0, -2, -2, 0], [4, 2, 4, 0], [-4, -4, 3, -3], [4, -4, 2, 2], [0, -4, 0, 0], [-4, -4, -4, -4], [-2, 0, 2, 2], [0, 2, 2, 0], [-4, 4, 1, 1], [4, 4, 6, -6], [6, 4, -4, -6], [0, 0, -2, 0], [0, 2, 6, 2], [4, 4, 4, 4], [0, 0, 1, 0], [-8, -3, 0, 3], [0, 0, 0, 0], [-4, 0, 0, -4], [5, -5, 2, 2], [0, -4, 4, 0], [10, 0, -10, -8], [0, 2, 0, 2], [2, -4, 2, 0], [7, 7, -1, 1], [-5, -5, 5, -5], [8, 8, 0, -8], [-4, 0, 0, -4], [6, 0, -6, -4], [-1, -2, 0, 2], [0, 0, 8, 0], [0, -4, 0, 4], [-10, 0, 10, 8], [4, 5, 5, 4], [0, 0, 0, 0], [2, 2, 0, 0], [2, 2, 2, -2], [0, -6, 0, 0], [-8, -2, 0, 2], [6, 0, -6, 4], [1, 7, -7, -1], [3, -3, -11, -11], [-6, 2, 2, -6], [-2, -3, 3, 2], [0, 4, 0, -4], [0, -7, 0, -7], [8, 8, 0, 0], [0, 2, 3, 2], [0, -2, -4, -2], [-1, 7, -7, 1], [-2, -2, -2, 2], [0, 0, 0, 0], [3, -5, -5, 3], [-6, 0, 6, 14], [-10, 2, -2, 10], [-8, 4, -8, 0], [-2, 2, 10, 10], [0, 0, 2, -2], [2, 0, 2, 0], [6, 10, 10, 6], [-6, -4, -6, 0], [4, -4, 0, 4], [-8, -8, 0, 0], [4, -2, 0, 2], [-1, 0, -1, 0], [-1, -12, -12, -1], [8, 0, -8, -6]]}