# Stored data for newform 1024.2.e.c, downloaded from the LMFDB on 19 April 2024.
{"label": "1024.2.e.c", "space_label": "1024.2.e", "level": 1024, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007474166203392, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 184739671611369557, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [2, 2, 1]], [5, [8, -4, 1]], [47, [0, 1]]], "qexp_display": "q+(-1+i)q^{3}+(2+2i)q^{5}+4iq^{7}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 16, "char_orbit_label": "e", "char_is_real": false, "Nk2": 4096, "analytic_conductor": 8.176681166979112, "hecke_ring_index": 1, "level_radical": 2, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": "0.261", "prec": 17}, "analytic_rank_proved": true, "char_values": [1024, 4, [1023, 5], [4, 3]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2], "conrey_indexes": [257, 769], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.005", "prec": 17}, {"__RealLiteral__": 0, "data": "0.057", "prec": 17}, {"__RealLiteral__": 0, "data": "12.218", "prec": 20}, {"__RealLiteral__": 0, "data": "1.262", "prec": 17}, {"__RealLiteral__": 0, "data": "103.814", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c4", "trace_display": [0, -2, 4, 0], "traces": [0, 2, 0, -2, 0, 4, 0, 0, 0, 0, 0, -2, 0, -4, 0, -8, 0, 8, 0, -10, 0, -8, 0, 0, 0, 0, 0, -8, 0, 12, 0, 16, 0, 4, 0, -16, 0, -4, 0, 0, 0, 0, 0, -6, 0, -4, 0, 0, 0, -18, 0, -8, 0, 4, 0, 0, 0, 0, 0, 6, 0, -12, 0, -8, 0, -16, 0, -6, 0, 8, 0, 0, 0, 0, 0, -6, 0, 8, 0, 16, 0, 10, 0, -14, 0, 16, 0, 0, 0, 0, 0, -16, 0, -16, 0, -40, 0, -8, 0, 2, 0, -4, 0, 0, 0, 0, 0, 14, 0, 20, 0, 8, 0, -28, 0, 16, 0, -4, 0, 0, 0, 0, 0, 4, 0, 8, 0, 16, 0, 12, 0, 10, 0, -40, 0, 0, 0, 0, 0, -6, 0, 0, 0, 8, 0, 48, 0, 18, 0, -4, 0, 0, 0, 0, 0, 32, 0, -12, 0, -8, 0, 32, 0, 14, 0, 8, 0, 0, 0, 0, 0, -10, 0, -20, 0, -24, 0, -12, 0, 2, 0, 12, 0, 0, 0, 0, 0, -8, 0, 32, 0, 16, 0, -8, 0, 16, 0, 20, 0, 0, 0, 0, 0, 48, 0, 8, 0, 8, 0, 20, 0, 34, 0, 8, 0, 0, 0, 0, 0, -8, 0, -16, 0, 48, 0, -6, 0, 30, 0, 36, 0, 0, 0, 0, 0, 0, 0, -16, 0, 16, 0, -24, 0, 14, 0, -36, 0, 0, 0, 0, 0, 6, 0, -8, 0, -32, 0, -4, 0, 16, 0, 12, 0, 0, 0, 0, 0, -24, 0, -28, 0, -64, 0, 32, 0, 6, 0, -12, 0, 0, 0, 0, 0, 34, 0, 40, 0, 16, 0, -2, 0, 8, 0, -12, 0, 0, 0, 0, 0, 16, 0, 24, 0, 8, 0, -48, 0, -10, 0, -24, 0, 0, 0, 0, 0, -16, 0, -4, 0, -24, 0, -28, 0, -40, 0, -12, 0, 0, 0, 0, 0, -18, 0, 4, 0, -24, 0, -60, 0, 28, 0, -16, 0, 0, 0, 0, 0, 22, 0, 28, 0, 32, 0, -28, 0, 16, 0, -32, 0, 0, 0, 0, 0, 18, 0, -16, 0, -32, 0, 4, 0, -16, 0, 52, 0, 0, 0, 0, 0, -42, 0, -16, 0, 32, 0, 32, 0, 6, 0, 28, 0, 0, 0, 0, 0, 32, 0, 4, 0, 80, 0, 72, 0, -32, 0, 20, 0, 0, 0, 0, 0, -36, 0, -24, 0, -56, 0, 12, 0, -38, 0, -12, 0, 0, 0, 0, 0, -48, 0, -8, 0, 48, 0, 40, 0, -48, 0, 40, 0, 0, 0, 0, 0, 50, 0, -48, 0, 8, 0, -40, 0, -4, 0, 8, 0, 0, 0, 0, 0, -32, 0, 20, 0, -16, 0, -64, 0, -26, 0, -24, 0, 0, 0, 0, 0, -30, 0, -4, 0, -48, 0, 16, 0, -32, 0, -16, 0, 0, 0, 0, 0, -22, 0, 48, 0, 8, 0, 32, 0, 18, 0, 24, 0, 0, 0, 0, 0, -10, 0, 4, 0, -32, 0, 80, 0, -48, 0, 0, 0, 0, 0, 0, 0, 14, 0, 24, 0, 64, 0, 14, 0, -6, 0, 8, 0, 0, 0, 0, 0, 18, 0, -12, 0, -24, 0, 80, 0, -38, 0, -12, 0, 0, 0, 0, 0, 16, 0, 44, 0, 24, 0, 16, 0, -10, 0, -56, 0, 0, 0, 0, 0, -46, 0, -16, 0, 24, 0, -36, 0, 8, 0, -56, 0, 0, 0, 0, 0, -2, 0, -80, 0, -40, 0, -36, 0, -64, 0, -8, 0, 0, 0, 0, 0, -6, 0, 36, 0, 0, 0, -96, 0, 0, 0, -12, 0, 0, 0, 0, 0, -2, 0, -32, 0, -96, 0, 62, 0, -20, 0, -16, 0, 0, 0, 0, 0, 32, 0, 36, 0, 8, 0, -8, 0, -6, 0, 24, 0, 0, 0, 0, 0, -64, 0, 68, 0, 40, 0, -8, 0, -46, 0, 44, 0, 0, 0, 0, 0, -48, 0, -48, 0, 24, 0, -40, 0, 24, 0, 60, 0, 0, 0, 0, 0, 42, 0, -72, 0, -72, 0, -16, 0, 66, 0, 8, 0, 0, 0, 0, 0, 24, 0, 68, 0, 40, 0, 0, 0, 16, 0, 12, 0, 0, 0, 0, 0, 16, 0, -16, 0, -48, 0, -96, 0, 24, 0, 36, 0, 0, 0, 0, 0, -24, 0, 28, 0, 72, 0, 12, 0, -34, 0, 40, 0, 0, 0, 0, 0, -14, 0, -56, 0, 80, 0, -12, 0, 16, 0, -36, 0, 0, 0, 0, 0, 80, 0, -16, 0, -24, 0, 88, 0, 4, 0, 12, 0, 0, 0, 0, 0, 20, 0, -8, 0, -96, 0, -48, 0, 66, 0, -56, 0, 0, 0, 0, 0, -16, 0, -28, 0, 0, 0, -24, 0, 8, 0, 64, 0, 0, 0, 0, 0, -34, 0, 64, 0, 56, 0, 60, 0, 16, 0, -12, 0, 0, 0, 0, 0, -30, 0, 36, 0, 24, 0, -72, 0, 48, 0, -64, 0, 0, 0, 0, 0, 40, 0, -20, 0, 72, 0, -68, 0, -16, 0, -60, 0, 0, 0, 0, 0, 54, 0, -16, 0, 48, 0, -80, 0, 2, 0, -16, 0, 0, 0, 0, 0, 32, 0, -12, 0, 24, 0, 68, 0, -58, 0, -24, 0, 0, 0, 0, 0, -10, 0, 0, 0, 8, 0, -32, 0, 96, 0, 16, 0, 0, 0, 0, 0, 10, 0, 4, 0, -96, 0, 28, 0, 48, 0, 40, 0, 0, 0, 0, 0, 16, 0, 12, 0, -24, 0, 120, 0, 90, 0, -40, 0, 0, 0, 0, 0, 28, 0, 52, 0, -16, 0, 128, 0, 86, 0, -16, 0, 0, 0, 0, 0, 32, 0, 24, 0, -144, 0, 66, 0, -14, 0, -16, 0, 0, 0, 0, 0, -22, 0, 24, 0, 24, 0, -24, 0, 24, 0, 20, 0, 0, 0, 0, 0, 0, 0, -24, 0, -64, 0, 36, 0, -16, 0, -20, 0, 0, 0, 0, 0, 24, 0, 24, 0, -40, 0, 8, 0, 60, 0, 60, 0, 0, 0, 0, 0, -46, 0, 12, 0, 32, 0, 12, 0, -32, 0, 16, 0, 0, 0, 0, 0, 16, 0, -48, 0, 64, 0, -44, 0, 16, 0, 40, 0, 0, 0, 0, 0, -26, 0, -20, 0, 136, 0, 32, 0, 28, 0, -68, 0, 0, 0, 0, 0, 8, 0, -68, 0, -32, 0, -48, 0, 18, 0, 72, 0, 0, 0, 0, 0, 62, 0, -128, 0, -32, 0, 18, 0, -2, 0, 68, 0, 0, 0, 0, 0, -48, 0, 32, 0, 64, 0, -64, 0, -16, 0, -4, 0, 0, 0, 0, 0, 96, 0, 20, 0, -104, 0, -60, 0, 46, 0, 8, 0, 0, 0, 0, 0, -48, 0, 24, 0, 120, 0, 84, 0, -24, 0, 56, 0, 0, 0, 0, 0, -32, 0, -32, 0, -32, 0, 36, 0, -32, 0, -48, 0, 0, 0, 0, 0, 58, 0, 48, 0, -56, 0, 96, 0, 6, 0, 32, 0, 0, 0, 0, 0, 10, 0, 44, 0, -40, 0, -64, 0, 46, 0, -24, 0, 0, 0, 0, 0, 32, 0, 40, 0, -40, 0, 28, 0, -72, 0, -48, 0, 0, 0, 0, 0, -80, 0, -12, 0, 56, 0, -60, 0, 16, 0, -8, 0, 0, 0, 0, 0, 28, 0, 44, 0, 80, 0, -36, 0, 80, 0, -76, 0, 0, 0, 0, 0, 28, 0, 56, 0, -72, 0, -68, 0, 6, 0, 8, 0, 0, 0, 0, 0, -82, 0, 16, 0, 24, 0, -32, 0, -48, 0, 0, 0, 0, 0, 0, 0, -24, 0, -84, 0, 96, 0, 96, 0, -50, 0, -8, 0, 0, 0, 0, 0, 62, 0, -48, 0, 64, 0, -88, 0, -40, 0, -84, 0, 0, 0, 0, 0, -46, 0, 32, 0, -80, 0, 16, 0, -112, 0, -8, 0, 0, 0, 0, 0, 72, 0, -12, 0, -48, 0, -100, 0, -40, 0, -48, 0, 0, 0, 0, 0, -48, 0, 4, 0, 64, 0, -112, 0, 40, 0, 40, 0, 0, 0, 0, 0, -128, 0, 24, 0, 8, 0, -24, 0, 0, 0, 64, 0, 0, 0, 0, 0, 4, 0, -36, 0, -16, 0, 40, 0, -80, 0, -28, 0, 0, 0, 0, 0, -40, 0, 16, 0, -56, 0, -32, 0, -32, 0, -16, 0, 0, 0, 0, 0, 48, 0, 80, 0, 48, 0, -72, 0, -56, 0, -12, 0, 0, 0, 0, 0, -12, 0, -108, 0, -112, 0, 60, 0, -10, 0, -12, 0, 0, 0, 0, 0, 32, 0, 48, 0, 128, 0, -20, 0, -16, 0, -4, 0, 0, 0, 0, 0, -102, 0, -60, 0, 32, 0, 0, 0, 6, 0, 24, 0, 0, 0, 0, 0, 14, 0, 56, 0, 0, 0, 44, 0, -18, 0, 136, 0, 0, 0, 0, 0, 42, 0, -32, 0, -48, 0, 72, 0, -32, 0, 28, 0, 0, 0, 0, 0, -62, 0, -80, 0, 24, 0, 96, 0, 36, 0, 40, 0, 0, 0, 0, 0, 16, 0, -8, 0, -144, 0, -10, 0, -78, 0, -36, 0, 0, 0, 0, 0, -30, 0, 32, 0, -40, 0, 48, 0, -50, 0, 24, 0, 0, 0, 0, 0, -64, 0, 44, 0, 0, 0, 68, 0, -80, 0, -20, 0, 0, 0, 0, 0, 28, 0, 56, 0, 16, 0, -28, 0, 74, 0, 36, 0, 0, 0, 0, 0, 106, 0, -64, 0, -16, 0, -16, 0, -14, 0, 120, 0, 0, 0, 0, 0, -48, 0, 60, 0, -16, 0, -92, 0, -144, 0, -56, 0, 0, 0, 0, 0, 2, 0, -44, 0, -160, 0, -36, 0, 2, 0, 44, 0, 0, 0, 0, 0, 6, 0, -12, 0, 96, 0, -32, 0, -80, 0, 76, 0, 0, 0, 0, 0, 32, 0, 0, 0, 96, 0, -32, 0, -32, 0, -120, 0, 0, 0, 0, 0, -64, 0, -8, 0, -160, 0, 16, 0, -2, 0, -84, 0, 0, 0, 0, 0, -18, 0, -24, 0, 32, 0, 74, 0, 8, 0, -120, 0, 0, 0, 0, 0, -120, 0, -68, 0, 112, 0, 120, 0, -6, 0, 56, 0, 0, 0, 0, 0, -60, 0, 84, 0, 72, 0, 92, 0, 32, 0, -16, 0, 0, 0, 0, 0, 70, 0, -24, 0, 24, 0, 160, 0, 36, 0, -84, 0, 0, 0, 0, 0, 0, 0, 28, 0, 112, 0, 112, 0, -90, 0, 8, 0, 0, 0, 0, 0, 64, 0, -24, 0, 32, 0, 4, 0, -12, 0, -56, 0, 0, 0, 0, 0, -32, 0, -20, 0, 24, 0, -4, 0, 36, 0, -72, 0, 0, 0, 0, 0, 34, 0, 20, 0, -8, 0, -28, 0, 144, 0, -72, 0, 0, 0, 0, 0, 8, 0, 124, 0, 24, 0, 48, 0, 54, 0, 36, 0, 0, 0, 0, 0, 56, 0, 0, 0, -144, 0, -24, 0, -48, 0, 48, 0, 0, 0, 0, 0, -64, 0, -24, 0, 24, 0, -224, 0, 40, 0, 8, 0, 0, 0, 0, 0, 56, 0, 80, 0, -64, 0, 4, 0, 10, 0, 52, 0, 0, 0, 0, 0, -6, 0, 96, 0, 0, 0, 8, 0, -62, 0, 100, 0, 0, 0, 0, 0, -112, 0, -96, 0, 32, 0, -36, 0, -96, 0, 8, 0, 0, 0, 0, 0, 34, 0, 36, 0, 40, 0, -64, 0, 86, 0, 56, 0, 0, 0, 0, 0, 64, 0, -32, 0, 40, 0, -112, 0, 8, 0, 24, 0, 0, 0, 0, 0, -2, 0, -76, 0, 24, 0, 16, 0, 48, 0, -24, 0, 0, 0, 0, 0, 12, 0, 36, 0, -16, 0, -64, 0, 64, 0, -120, 0, 0, 0, 0, 0, 16, 0, -40, 0, 160, 0, -4, 0, 32, 0, -4, 0, 0, 0, 0, 0, -62, 0, -136, 0, -88, 0, 16, 0, 42, 0, -16, 0, 0, 0, 0, 0, 160, 0, -20, 0, -128, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 16, 5, 1, 4, 0]], "char_orbit_index": 5, "prim_orbit_index": 5, "minimal_twist": "512.2.a.c", "char_is_minimal": false, "conrey_index": 257, "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], [1, 0], [0, 0], [-1, 1], [0, 0], [2, 2], [0, 0], [0, 4], [0, 0], [0, 1], [0, 0], [-1, -1], [0, 0], [-2, 2], [0, 0], [-4, 0], [0, 0], [4, 0], [0, 0], [-5, 5], [0, 0], [-4, -4], [0, 0], [0, -4], [0, 0], [0, 3], [0, 0], [-4, -4], [0, 0], [6, -6], [0, 0], [8, 0], [0, 0], [2, 0], [0, 0], [-8, 8], [0, 0], [-2, -2], [0, 0], [0, -4], [0, 0], [0, -2], [0, 0], [-3, -3], [0, 0], [-2, 2], [0, 0], [0, 0], [0, 0], [-9, 0], [0, 0], [-4, 4], [0, 0], [2, 2], [0, 0], [0, -4], [0, 0], [0, -10], [0, 0], [3, 3], [0, 0], [-6, 6], [0, 0], [-4, 0], [0, 0], [-8, 0], [0, 0], [-3, 3], [0, 0], [4, 4], [0, 0], [0, -4], [0, 0], [0, 4], [0, 0], [-3, -3], [0, 0], [4, -4], [0, 0], [8, 0], [0, 0], [5, 0], [0, 0], [-7, 7], [0, 0], [8, 8], [0, 0], [0, 12], [0, 0], [0, 12], [0, 0], [-8, -8], [0, 0], [-8, 8], [0, 0], [-20, 0], [0, 0], [-4, 0], [0, 0], [1, -1], [0, 0]]}