# Stored data for newform 1280.2.o.p, downloaded from the LMFDB on 20 April 2024. {"label": "1280.2.o.p", "space_label": "1280.2.o", "level": 1280, "weight": 2, "hecke_orbit": 16, "hecke_orbit_code": 67554956516787456, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 1869490945040859918, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [8, -4, 1]], [7, [8, -4, 1]], [13, [2, 2, 1]]], "qexp_display": "q+(2-2i)q^{3}+(1+2i)q^{5}+(2-2i)q^{7}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 40, "char_orbit_label": "o", "char_is_real": false, "Nk2": 5120, "analytic_conductor": 10.220851458723889, "hecke_ring_index": 1, "level_radical": 10, "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": "0.254", "prec": 17}, "analytic_rank_proved": true, "char_values": [1280, 4, [511, 261, 257], [2, 2, 1]], "hecke_ring_generator_nbound": 9, "inner_twist_count": 2, "level_primes": [2, 5], "conrey_indexes": [127, 383], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.035", "prec": 17}, {"__RealLiteral__": 0, "data": "2.001", "prec": 17}, {"__RealLiteral__": 0, "data": "0.036", "prec": 17}, {"__RealLiteral__": 0, "data": "12.237", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "105.087", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c4", "trace_display": [0, 4, 2, 4], "traces": [0, 2, 0, 4, 0, 2, 0, 4, 0, 0, 0, 0, 0, -2, 0, 12, 0, -10, 0, 0, 0, 0, 0, 4, 0, -6, 0, -8, 0, 8, 0, 0, 0, 0, 0, 12, 0, 2, 0, -8, 0, 0, 0, 12, 0, 20, 0, 4, 0, 0, 0, -40, 0, 14, 0, 0, 0, -16, 0, 0, 0, 0, 0, -20, 0, 2, 0, 20, 0, 16, 0, 0, 0, 6, 0, 4, 0, 0, 0, -32, 0, -2, 0, -4, 0, 10, 0, 16, 0, 0, 0, -8, 0, 16, 0, 16, 0, -6, 0, 0, 0, 0, 0, -12, 0, 32, 0, 12, 0, -20, 0, 0, 0, -18, 0, -4, 0, -10, 0, -40, 0, -22, 0, 0, 0, -22, 0, -20, 0, 0, 0, 16, 0, -16, 0, 8, 0, -2, 0, 0, 0, 0, 0, 0, 0, 8, 0, -4, 0, -36, 0, 0, 0, -50, 0, -16, 0, 18, 0, 56, 0, 16, 0, 4, 0, 0, 0, -4, 0, 0, 0, -40, 0, 26, 0, 4, 0, 16, 0, 0, 0, 0, 0, -16, 0, 6, 0, 0, 0, -32, 0, 0, 0, -10, 0, -8, 0, 10, 0, 48, 0, 80, 0, 16, 0, 0, 0, 20, 0, 0, 0, 32, 0, 48, 0, 36, 0, 16, 0, 0, 0, 0, 0, 20, 0, 40, 0, -20, 0, -40, 0, 0, 0, 10, 0, 12, 0, -64, 0, -16, 0, -32, 0, 20, 0, 4, 0, -8, 0, 0, 0, 48, 0, 0, 0, -40, 0, 14, 0, 0, 0, 0, 0, 12, 0, -14, 0, 0, 0, 20, 0, 0, 0, -16, 0, 0, 0, -18, 0, 40, 0, -16, 0, -12, 0, 16, 0, 0, 0, 0, 0, -24, 0, 10, 0, -16, 0, 0, 0, 0, 0, 0, 0, 24, 0, 16, 0, 20, 0, -48, 0, 0, 0, -30, 0, 20, 0, -22, 0, 0, 0, 48, 0, -40, 0, 14, 0, -40, 0, 0, 0, 0, 0, -10, 0, -20, 0, -46, 0, 0, 0, 0, 0, 24, 0, 16, 0, 36, 0, -40, 0, 0, 0, 18, 0, -48, 0, -80, 0, -32, 0, 6, 0, -44, 0, 18, 0, 44, 0, 0, 0, 56, 0, -42, 0, -52, 0, -8, 0, 0, 0, 0, 0, -44, 0, 0, 0, -60, 0, 36, 0, 0, 0, 32, 0, -32, 0, -26, 0, -64, 0, 68, 0, 8, 0, -2, 0, 0, 0, 0, 0, -8, 0, 16, 0, -12, 0, -48, 0, 0, 0, 0, 0, -20, 0, 70, 0, -16, 0, 0, 0, 0, 0, -38, 0, 48, 0, 16, 0, -32, 0, -10, 0, -44, 0, 0, 0, -72, 0, 0, 0, 0, 0, 48, 0, -8, 0, -30, 0, 0, 0, 0, 0, 44, 0, -16, 0, -4, 0, 80, 0, 0, 0, 0, 0, 32, 0, 70, 0, 48, 0, -4, 0, 32, 0, 6, 0, -12, 0, 0, 0, 32, 0, -40, 0, 0, 0, 48, 0, 0, 0, 0, 0, 20, 0, -24, 0, -44, 0, -72, 0, 0, 0, -32, 0, 12, 0, 0, 0, 104, 0, -12, 0, -28, 0, 64, 0, 40, 0, 0, 0, 40, 0, 0, 0, -12, 0, -48, 0, 0, 0, 0, 0, 40, 0, -20, 0, 12, 0, -40, 0, 0, 0, -64, 0, 16, 0, 30, 0, -24, 0, 0, 0, -12, 0, -54, 0, -4, 0, 0, 0, 32, 0, 80, 0, -28, 0, 30, 0, 0, 0, 0, 0, 0, 0, -30, 0, -28, 0, 32, 0, 0, 0, 2, 0, -40, 0, 96, 0, -16, 0, 16, 0, 100, 0, -22, 0, 36, 0, 0, 0, -8, 0, 18, 0, 0, 0, 58, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, -20, 0, 0, 0, 64, 0, -60, 0, -2, 0, 120, 0, -96, 0, -20, 0, 96, 0, 20, 0, 0, 0, 64, 0, 2, 0, 16, 0, -30, 0, 0, 0, 0, 0, 40, 0, 16, 0, 16, 0, 80, 0, 0, 0, 10, 0, 56, 0, -6, 0, -24, 0, -80, 0, 44, 0, 2, 0, -80, 0, 0, 0, -64, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, -8, 0, 32, 0, 24, 0, -24, 0, 0, 0, -16, 0, 0, 0, -32, 0, -16, 0, -48, 0, -64, 0, -24, 0, 36, 0, 0, 0, -120, 0, 42, 0, 4, 0, 0, 0, 0, 0, 0, 0, 60, 0, -36, 0, 20, 0, 48, 0, 0, 0, 96, 0, -48, 0, -2, 0, 0, 0, 44, 0, -40, 0, -150, 0, 8, 0, 0, 0, 56, 0, 2, 0, -32, 0, -16, 0, 0, 0, 0, 0, -32, 0, 54, 0, -60, 0, 48, 0, 0, 0, -8, 0, 56, 0, 58, 0, -40, 0, 0, 0, 0, 0, 16, 0, 40, 0, 0, 0, 48, 0, -80, 0, 12, 0, -48, 0, 0, 0, 0, 0, -60, 0, 0, 0, 4, 0, -12, 0, 0, 0, -10, 0, -12, 0, 32, 0, -48, 0, -26, 0, -32, 0, 44, 0, -44, 0, 0, 0, 8, 0, -30, 0, -40, 0, 14, 0, 0, 0, 0, 0, -68, 0, -26, 0, 132, 0, 0, 0, 0, 0, -30, 0, -52, 0, -30, 0, 40, 0, -80, 0, 20, 0, -16, 0, 20, 0, 0, 0, 0, 0, -16, 0, 48, 0, -16, 0, 0, 0, 0, 0, -96, 0, -40, 0, 12, 0, 60, 0, 0, 0, 0, 0, 16, 0, 32, 0, -48, 0, 80, 0, 24, 0, 2, 0, -60, 0, 0, 0, -8, 0, -112, 0, 0, 0, -54, 0, 0, 0, 0, 0, 0, 0, -32, 0, 20, 0, -12, 0, 0, 0, 18, 0, -80, 0, 0, 0, -8, 0, 30, 0, 60, 0, -30, 0, -20, 0, 0, 0, -16, 0, -48, 0, 24, 0, 42, 0, 0, 0, 0, 0, -68, 0, 30, 0, -32, 0, 48, 0, 0, 0, 0, 0, 48, 0, -42, 0, -16, 0, 0, 0, 40, 0, 80, 0, 56, 0, 0, 0, -184, 0, 82, 0, 48, 0, 90, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 96, 0, 0, 0, 54, 0, 60, 0, -40, 0, 16, 0, 144, 0, -72, 0, 0, 0, -80, 0, 0, 0, -80, 0, 2, 0, 32, 0, 48, 0, 0, 0, 0, 0, 36, 0, -48, 0, 0, 0, -12, 0, 0, 0, 8, 0, 12, 0, -64, 0, 8, 0, 16, 0, 12, 0, -16, 0, 12, 0, 0, 0, 0, 0, -2, 0, 48, 0, -10, 0, 0, 0, 0, 0, -4, 0, -40, 0, 0, 0, -24, 0, 0, 0, 112, 0, -20, 0, 62, 0, -168, 0, 32, 0, 12, 0, -20, 0, 4, 0, 0, 0, -32, 0, 0, 0, 20, 0, 112, 0, 0, 0, 0, 0, 100, 0, -40, 0, 8, 0, -176, 0, 0, 0, -2, 0, 0, 0, 0, 0, -32, 0, -96, 0, 20, 0, 30, 0, 72, 0, 0, 0, 16, 0, -80, 0, 4, 0, 0, 0, 0, 0, 0, 0, -44, 0, -192, 0, -76, 0, 0, 0, 0, 0, -38, 0, -16, 0, -80, 0, 0, 0, 80, 0, 136, 0, -32, 0, 120, 0, 0, 0, 104, 0, -78, 0, 60, 0, -30, 0, 0, 0, 0, 0, 36, 0, 8, 0, -8, 0, -120, 0, 0, 0, -10, 0, -24, 0, -10, 0, 64, 0, -60, 0, 0, 0, -32, 0, 48, 0, 0, 0, -120, 0, -48, 0, 48, 0, 48, 0, 0, 0, 0, 0, -80, 0, 0, 0, 40, 0, -32, 0, 0, 0, 80, 0, 120, 0, 66, 0, -32, 0, -64, 0, 28, 0, -14, 0, 0, 0, 0, 0, 0, 0, -16, 0, 16, 0, -26, 0, 0, 0, 0, 0, -36, 0, 80, 0, 84, 0, 0, 0, 0, 0, 12, 0, -12, 0, -64, 0, 48, 0, 32, 0, -8, 0, -98, 0, -36, 0, 0, 0, 0, 0, 48, 0, 0, 0, 80, 0, 0, 0, 0, 0, 160, 0, 20, 0, -104, 0, 96, 0, 0, 0, 0, 0, 80, 0, -16, 0, 120, 0, -36, 0, 16, 0, -48, 0, -20, 0, 0, 0, -120, 0, 14, 0, 0, 0, 10, 0, 0, 0, 0, 0, -56, 0, -54, 0, -24, 0, 176, 0, 0, 0, 96, 0, 40, 0, 0, 0, 80, 0, -16, 0, 16, 0, -16, 0, 160, 0, 0, 0, 40, 0, -90, 0, -36, 0, 20, 0, 0, 0, 0, 0, -12, 0, 112, 0, 20, 0, -28, 0, 0, 0, -74, 0, 0, 0, 96, 0, -144, 0, 0, 0, -8, 0, -132, 0, 44, 0, 0, 0, -96, 0, -18, 0, -24, 0, 16, 0, 0, 0, 0, 0, 0, 0, -10, 0, -20, 0, 36, 0, 0, 0, 64, 0, -32, 0, 64, 0, -160, 0, -80, 0, -20, 0, 0, 0, -100, 0, 0, 0, 192, 0, 62, 0, 16, 0, -16, 0, 0, 0, 0, 0, 20, 0, 96, 0, 0, 0, 80, 0, 0, 0, 0, 0, -24, 0, 0, 0, 8, 0, -110, 0, 12, 0, 32, 0, -144, 0, 0, 0, 80, 0, -48, 0, -20, 0, 56, 0, 0, 0, 0, 0, 28, 0, -48, 0, 40, 0, 152, 0, 0, 0, -78, 0, 112, 0, 130, 0, -128, 0, 80, 0, -24, 0, -90, 0, 12, 0, 0, 0, -112, 0, 22, 0, 140, 0, 16, 0, 0, 0, 0, 0, -20, 0, -66, 0, -60, 0, -80, 0, 0, 0, 32, 0, 0, 0, -58, 0, 0, 0, -92, 0, -80, 0, 48, 0, -44, 0, 0, 0, -120, 0, 10, 0, -120, 0, 0, 0, 0, 0, 0, 0, -120, 0, 18, 0, 20, 0, 100, 0, 0, 0, -48, 0, -120, 0, 110, 0, 0, 0, 48, 0, -56, 0, 32, 0, -32, 0, 0, 0, 40, 0, -64, 0, 0, 0, 2, 0, 0, 0, 0, 0, 60, 0, 10, 0, -4, 0, -8, 0, 0, 0, -32, 0, -140, 0, -48, 0, 24, 0, -82, 0, 0, 0, 46, 0, -64, 0, 0, 0, 0, 0, 6, 0, -144, 0, 70, 0, 0, 0, 0, 0, -16, 0, 0, 0, 8, 0, -72, 0, 0, 0, 64, 0, -24, 0, 60, 0, 200, 0, 20, 0, -76, 0, -48, 0, 0, 0, 0, 0, 120, 0, -6, 0, -36, 0, 50, 0, 0, 0, 0, 0, 32, 0, -40, 0, 44, 0, 0, 0, 0, 0, 42, 0, -32, 0, 96, 0, -16, 0, -112, 0, 0, 0, 54, 0, 64, 0, 0, 0, 0, 0, -50, 0, -96, 0, -66, 0, 0, 0, 0, 0, -4, 0, -240, 0, -52, 0, 40, 0, 0, 0, 0, 0, -32, 0, -32, 0, 56, 0, -112, 0, 32, 0, 6, 0, -24, 0, 0, 0, 144, 0, -2, 0, -132, 0, -64, 0, 0, 0, 0, 0, 12, 0, 6, 0, -80, 0, -32, 0, 0, 0, -16, 0, 132, 0, 0, 0, 72, 0, 48, 0, -24, 0, 0, 0, -4, 0, 0, 0, 232, 0, 100, 0, 56, 0, -112, 0, 0, 0, 0, 0, -4, 0, 42, 0, 84, 0, 0, 0, 0, 0, 86, 0, -124, 0, -38, 0, -64, 0, 0, 0, 40, 0, 8, 0, -40, 0, 0, 0, 32, 0, 16, 0, -112, 0, -80, 0, 0, 0, 0, 0, 0, 0, -160, 0, 100, 0, -16, 0, 0, 0, 54, 0, 44, 0, 96, 0, 48, 0, 180, 0, -192, 0, 0, 0, 0, 0, 0, 0, 32, 0, 42, 0, 60, 0, 36, 0, 0, 0, 0, 0, 80, 0, 36, 0, 0, 0, -84, 0, 0, 0, 80, 0, 80, 0, -48, 0, 8, 0, 28, 0, 24, 0, 96, 0, -32, 0, 0, 0, -48, 0, -22, 0, 96, 0, -80, 0, 0, 0, 0, 0, -48, 0, -78, 0, -68, 0, 100, 0, 0, 0, 78, 0, -64, 0, 82, 0, 144, 0], "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, 40, 11, 1, 4, 0]], "char_orbit_index": 15, "prim_orbit_index": 11, "minimal_twist": "160.2.n.a", "char_is_minimal": false, "conrey_index": 127, "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], [2, -2], [0, 0], [1, 2], [0, 0], [2, -2], [0, 0], [0, -5], [0, 0], [0, 0], [0, 0], [-1, -1], [0, 0], [6, 2], [0, 0], [-5, -5], [0, 0], [0, -4], [0, 0], [0, -8], [0, 0], [2, 2], [0, 0], [-3, 4], [0, 0], [-4, -4], [0, 0], [4, 0], [0, 0], [0, 4], [0, 0], [0, 0], [0, 0], [6, 2], [0, 0], [1, -1], [0, 0], [-4, 0], [0, 0], [0, 0], [0, 0], [6, -6], [0, 0], [10, -5], [0, 0], [2, -2], [0, 0], [0, -1], [0, 0], [-20, 0], [0, 0], [7, 7], [0, 0], [0, 0], [0, 0], [-8, -8], [0, 0], [0, 4], [0, 0], [0, -4], [0, 0], [-10, -10], [0, 0], [1, -3], [0, 0], [10, 10], [0, 0], [8, 0], [0, 0], [0, 12], [0, 0], [3, -3], [0, 0], [2, 14], [0, 0], [0, 0], [0, 0], [-16, 0], [0, 0], [-1, 0], [0, 0], [-2, 2], [0, 0], [5, -15], [0, 0], [8, -8], [0, 0], [0, 0], [0, 0], [-4, 0], [0, 0], [8, 8], [0, 0], [8, -4], [0, 0], [-3, -3], [0, 0], [0, 0], [0, 0]]}