# Stored data for newform 2646.2.f.k, downloaded from the LMFDB on 23 April 2024. {"label": "2646.2.f.k", "space_label": "2646.2.f", "level": 2646, "weight": 2, "hecke_orbit": 11, "hecke_orbit_code": 45036339904645718, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.1", "trace_hash": 1936156652243565443, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [25, -10, 9, 2, 1]], [11, [4, -2, 1]], [13, [576, 0, 24, 0, 1]]], "qexp_display": "q+(1-\\beta _{1})q^{2}-\\beta _{1}q^{4}+(-\\beta _{1}+\\beta _{2}+\\cdots)q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "f", "char_is_real": false, "Nk2": 10584, "analytic_conductor": 21.12841637483079, "hecke_ring_index": 3, "level_radical": 42, "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": "0.028", "prec": 17}, "analytic_rank_proved": true, "char_values": [2646, 3, [785, 1081], [2, 3]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [883, 1765], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, -2, 0, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.864", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "56.864", "prec": 20}, {"__RealLiteral__": 0, "data": "1.703", "prec": 17}, {"__RealLiteral__": 0, "data": "1399.591", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c3", "trace_display": [2, 0, -2, 0], "traces": [0, 4, 2, 0, -2, -2, 0, 0, -4, 0, -4, 4, 0, 0, 0, 0, -2, 8, 0, -20, -2, 0, -4, -2, 0, -4, 0, 0, 0, -4, 0, 12, 2, 0, 4, 0, 0, 8, -10, 0, 2, 0, 0, -4, -8, 0, -4, 0, 0, 0, 4, 0, 0, 24, 0, -8, 0, 0, 4, 4, 0, 18, 24, 0, 4, -24, 0, 16, -4, 0, 0, -20, 0, 8, 4, 0, 10, 0, 0, -6, 4, 0, 0, -4, 0, -4, 4, 0, -4, -48, 0, 0, -2, 0, 0, 22, 0, -4, 0, 0, 8, 10, 0, 28, 0, 0, 12, 48, 0, -8, -4, 0, 0, -22, 0, -2, 8, 0, 8, 0, 0, 14, -18, 0, 12, 36, 0, -12, 2, 0, 24, 22, 0, 0, 32, 0, -8, -4, 0, 14, 0, 0, -10, 0, 0, -40, 4, 0, -4, -12, 0, 10, 20, 0, 0, 12, 0, -2, 6, 0, 2, 0, 0, -40, 0, 0, 4, -8, 0, -22, -8, 0, 8, 16, 0, 0, 4, 0, -24, -24, 0, 12, 0, 0, 2, 44, 0, 8, 0, 0, 44, 18, 0, 26, 4, 0, 0, -8, 0, -8, 4, 0, -10, 0, 0, 48, 56, 0, 0, -20, 0, -16, -12, 0, 24, -40, 0, 0, -4, 0, 4, 0, 0, -32, 0, 0, -44, 6, 0, -22, 2, 0, 4, 28, 0, -96, 4, 0, 0, -6, 0, -8, 28, 0, -36, 0, 0, 24, -12, 0, 18, 60, 0, -8, -6, 0, -2, -36, 0, 0, 48, 0, 44, 42, 0, 12, 0, 0, 16, -44, 0, -48, -4, 0, 4, 8, 0, 8, 28, 0, 0, -38, 0, -46, 10, 0, 0, 0, 0, -52, -20, 0, -4, -30, 0, 4, -8, 0, -24, 0, 0, 0, -10, 0, 10, -60, 0, -52, 0, 0, -12, -32, 0, 20, -4, 0, 12, 12, 0, 8, -2, 0, 0, -40, 0, 96, -20, 0, 0, 0, 0, 20, 8, 0, -16, -8, 0, -12, 22, 0, -4, 48, 0, 0, 4, 0, -16, 0, 0, 32, 0, 0, 8, 12, 0, 34, 24, 0, -12, -4, 0, 48, 6, 0, 0, 20, 0, -8, 4, 0, 88, 0, 0, 4, -8, 0, 0, -96, 0, -8, 22, 0, -18, -4, 0, 0, 52, 0, 8, -40, 0, -4, 0, 0, -4, 60, 0, -96, -4, 0, -4, -30, 0, 0, -20, 0, 0, 8, 0, -8, -48, 0, 28, 0, 0, 8, 0, 0, 20, -54, 0, -36, -32, 0, -24, -8, 0, 0, -24, 0, -20, -48, 0, -8, 0, 0, 4, 10, 0, 24, 8, 0, 0, -20, 0, 0, 32, 0, 0, -4, 0, 0, -22, 0, -6, 0, 0, -14, -44, 0, 4, -26, 0, 22, -4, 0, 14, 40, 0, 0, -48, 0, -4, 8, 0, 44, 0, 0, -12, 20, 0, 96, 8, 0, 14, 56, 0, -28, -18, 0, 0, 12, 0, -8, 48, 0, -24, 0, 0, -8, -18, 0, 30, 0, 0, 100, -4, 0, 6, 24, 0, 0, -4, 0, -72, 28, 0, 0, 0, 0, 24, -96, 0, 28, 22, 0, -42, 24, 0, 44, 24, 0, 0, 96, 0, -24, -16, 0, -22, 0, 0, 24, -24, 0, 4, 76, 0, -24, 8, 0, 16, -4, 0, 0, -8, 0, 14, 32, 0, -96, 0, 0, 38, 26, 0, -46, -92, 0, 20, -60, 0, -48, 0, 0, 0, 8, 0, -16, -26, 0, 20, 0, 0, 24, -8, 0, -60, 2, 0, -60, -4, 0, -4, 0, 0, 0, -12, 0, 0, -48, 0, 4, 0, 0, -20, 14, 0, 12, -10, 0, -30, -192, 0, 0, -26, 0, 0, 28, 0, 26, -24, 0, -64, 0, 0, 14, -20, 0, -2, 16, 0, 92, 6, 0, -12, 6, 0, 0, 16, 0, -4, 34, 0, -20, 0, 0, -20, -144, 0, 16, 48, 0, 20, 0, 0, 34, 0, 0, 0, -20, 0, 14, -20, 0, 4, 0, 0, 8, -8, 0, 8, -36, 0, -22, -24, 0, 44, 0, 0, 0, 4, 0, 24, -168, 0, 104, 0, 0, -4, 48, 0, 58, -32, 0, 0, 26, 0, 0, -32, 0, 0, -88, 0, 56, 4, 0, -12, 0, 0, -16, 68, 0, 48, 12, 0, 48, 12, 0, -2, 0, 0, 0, 24, 0, -6, 40, 0, 32, 0, 0, 40, -8, 0, -30, 8, 0, 2, 64, 0, -24, 44, 0, 0, 72, 0, -12, 8, 0, -16, 0, 0, -42, 0, 0, -48, -20, 0, -24, -4, 0, -22, -4, 0, 0, -36, 0, -8, 0, 0, 20, 0, 0, 26, 28, 0, -48, 4, 0, 40, -48, 0, -20, -8, 0, 0, 34, 0, 36, 4, 0, 30, 0, 0, -48, -48, 0, 4, -18, 0, 0, -8, 0, -60, 8, 0, 0, 0, 0, -10, 104, 0, 8, 0, 0, -8, -28, 0, -4, -16, 0, -96, 40, 0, -32, -28, 0, 0, 48, 0, -64, 4, 0, 0, 0, 0, -80, 40, 0, -108, 80, 0, 2, 36, 0, -16, 44, 0, 0, -12, 0, 8, -4, 0, -14, 0, 0, -48, 60, 0, -20, 20, 0, -24, -28, 0, -80, -4, 0, 0, 12, 0, -48, 8, 0, 20, 0, 0, 4, -24, 0, 4, 0, 0, -40, 0, 0, 20, 48, 0, 0, 0, 0, 64, -48, 0, -60, 0, 0, -2, -48, 0, 48, 0, 0, 22, 30, 0, 24, -12, 0, 0, 6, 0, 8, 14, 0, -22, 0, 0, -44, 2, 0, 26, 48, 0, 88, 44, 0, -8, 0, 0, 0, -14, 0, 20, -16, 0, -104, 0, 0, 48, -2, 0, 0, -8, 0, 16, 56, 0, 48, -44, 0, 0, -104, 0, -84, -6, 0, -20, 0, 0, -10, 192, 0, 16, 2, 0, -10, -14, 0, 28, -108, 0, 0, -14, 0, 18, -36, 0, -48, 0, 0, 24, -12, 0, -68, 8, 0, 24, 8, 0, 32, -12, 0, 0, 28, 0, 70, -16, 0, -36, 0, 0, 8, -30, 0, 0, -72, 0, -136, 50, 0, 4, -6, 0, 0, 12, 0, 48, 44, 0, 26, 0, 0, -2, -192, 0, 96, -36, 0, -28, 54, 0, 54, 0, 0, 0, 36, 0, -24, -24, 0, -48, 0, 0, 88, 14, 0, -22, 40, 0, 12, -84, 0, 48, 8, 0, 0, -44, 0, 12, 16, 0, 136, 0, 0, -96, 8, 0, -2, -48, 0, -32, -104, 0, 40, 22, 0, 0, 0, 0, 0, 12, 0, 24, 0, 0, 66, 8, 0, 152, -4, 0, 28, 24, 0, 4, 88, 0, 0, 8, 0, 4, 38, 0, -48, 0, 0, -16, -48, 0, -20, -14, 0, 16, 112, 0, 120, -48, 0, 0, -20, 0, -62, 76, 0, 52, 0, 0, 42, 46, 0, -46, 112, 0, 12, 10, 0, 60, 32, 0, 0, -96, 0, 0, -82, 0, 24, 0, 0, 4, 144, 0, 32, -8, 0, 26, -48, 0, -102, 40, 0, 0, -36, 0, -14, -24, 0, -4, 0, 0, 112, -30, 0, -2, 96, 0, 48, -120, 0, -8, -46, 0, 0, 4, 0, 0, 72, 0, 192, 0, 0, 12, 8, 0, -54, 0, 0, -96, -8, 0, 26, -4, 0, 0, 64, 0, -40, -10, 0, -14, 0, 0, 16, 24, 0, -20, 12, 0, -12, 30, 0, -96, -144, 0, 0, 0, 0, 26, 60, 0, 12, 0, 0, 56, 144, 0, -2, -26, 0, -12, 16, 0, -88, -32, 0, 0, -56, 0, 0, 28, 0, -40, 0, 0, -18, 2, 0, 8, -108, 0, 96, 46, 0, -6, 4, 0, 0, -24, 0, 12, 0, 0, -56, 0, 0, 8, 36, 0, 136, -2, 0, -34, -48, 0, -84, -40, 0, 0, -12, 0, -26, 20, 0, -72, 0, 0, 68, 8, 0, -48, 16, 0, 72, 40, 0, 0, 70, 0, 0, -34, 0, 0, 240, 0, -36, 0, 0, 20, 96, 0, -20, 28, 0, -40, 24, 0, -86, -4, 0, 0, 144, 0, -48, 4, 0, 8, 0, 0, 0, 16, 0, -72, -12, 0, -14, 22, 0, -12, 148, 0, 0, 22, 0, 0, 48, 0, 4, 0, 0, 8, -64, 0, -96, -24, 0, -84, 64, 0, 252, 52, 0, 0, 64, 0, 36, -8, 0, 96, 0, 0, -104, -58, 0, -16, 128, 0, 8, 0, 0, -26, 0, 0, 0, 0, 0, -64, -12, 0, 44, 0, 0, -44, -36, 0, 76, 28, 0, -4, 18, 0, -8, -24, 0, 0, -34, 0, 144, 16, 0, 34, 0, 0, -224, 24, 0, -12, -60, 0, 56, 96, 0, 24, 8, 0, 0, 2, 0, 0, -4, 0, 88, 0, 0, -24, 26, 0, 24, -12, 0, 80, -24, 0, 72, -32, 0, 0, 0, 0, -76, 20, 0, 8, 0, 0, -90, -60, 0, 16, -48, 0, 58, -2, 0, 32, -16, 0, 0, -12, 0, -44, 36, 0, 58, 0, 0, 144, 36, 0, -88, 12, 0, 4, 24, 0, 48, -8, 0, 0, -72, 0, 54, -84, 0, 0, 0, 0, 8, 48, 0, -10, 40, 0, -96, -12, 0, 4, -192, 0, 0, -44, 0, -8, 136, 0, 60, 0, 0, -18, 56, 0, -8, -4, 0, 0, -34, 0, -72, 40, 0, 0, 16, 0, 40, -26, 0, 14, 0, 0, 24, -24, 0, -4, -28, 0, 40, 80, 0, -96, 96, 0, 0, 20, 0, -4, -184, 0, -120, 0, 0, -34, -106, 0, 0, 72, 0, 8, 20, 0, -64, -30, 0, 0, 60, 0, 120, -24, 0, 48, 0, 0, -104, 8, 0, -36, -40, 0, 64, 0, 0, -4, 48, 0, 0, -30, 0, -8, -90, 0, 8, 0, 0, 0, 128, 0, 44, 10, 0, 52, -80, 0, 8, 4, 0, 0, 24, 0, 6, -16, 0, -56, 0, 0, 10, 4, 0, -8, 28, 0, -48, -48, 0, -40, 72, 0, 0, -64, 0, -56, -8, 0, 0, 0, 0, 24, -184, 0, 64, -32, 0, -4, -20, 0, -32, 0, 0, 0, 32, 0, 32, 80, 0, 20, 0, 0, 32, -54, 0, -80, -4, 0, -110, 4, 0, 72, -156, 0, 0, 16, 0, 22, 192, 0, -220, 0, 0, 12, 120, 0, -100, 16, 0, -8, 24, 0, -24, 14, 0, 0, -120, 0, -16, -24, 0, -60, 0, 0, 20, -40, 0, 40, -8, 0, -80, 24, 0, -14, -8, 0, 0, -40, 0, 4, -24, 0, -96, 0, 0, 24, -192, 0, -24, 48, 0, 4, -112, 0, 32, 10, 0, 0, 56, 0, -72, 8, 0, -48, 0, 0, -64, -4, 0, 0, 192, 0, -24, -20, 0, 0, 12, 0, 0, 40, 0, 96, 68, 0, -4, 0, 0, 0, 192, 0, 48, 32, 0, 48, 40, 0, -60, -120, 0, 0, -40, 0, 50, 2, 0, -24, 0, 0, 40, 24, 0, 0, -144, 0, 24, 44, 0, 60, 30, 0, 0, -24, 0, -6, 12, 0, 96, 0, 0, -6, -24, 0, 40, 16, 0, 28, -24, 0, 48, 22, 0, 0, -80, 0, -32, -22, 0, -2, 0, 0, 44, 52, 0, 96, 36, 0, 30, -88, 0, 22, -16, 0, 0, -4, 0, 0, 44, 0, -38, 0, 0, -28, -20, 0, 18, -20, 0, -8, -68, 0, 84, -52, 0, 0, -80, 0, 28, 96, 0, -4, 0, 0, 0, 0, 0, -4, 264, 0, 216, 8, 0, -56, 124, 0, 0, 96, 0, -88, 0, 0, -32, 0, 0, -52, 276, 0, 8, -42, 0, 6, -18, 0, -28, -40, 0, 0, 10, 0, -44, 10, 0, 96, 0, 0, 384, 8, 0, -2, 28, 0, -28, -20, 0, -28, 0, 0, 0, -28, 0, -54, -160, 0, 32, 0, 0, 14, -114, 0, -68, 36, 0, -72, -4, 0, -140, 48, 0, 0, 240, 0, 0, 12, 0, 12, 0, 0, -24, -136, 0, 16, -54, 0, -60, -24, 0, 4, -264, 0, 0, 16, 0, 12, -24, 0, 12, 0, 0, 56, 12, 0, 56, -70, 0, -8, 144, 0, 148, -18], "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, 9, 3, 1, 3, 0]], "char_orbit_index": 6, "prim_orbit_index": 3, "minimal_twist": "126.2.f.c", "char_is_minimal": false, "conrey_index": 883, "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], [1, -1, 0, 0], [0, 0, 0, 0], [0, -1, 0, 0], [0, -1, 1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, 1], [2, -2, 0, 0], [0, 0, 0, 0], [0, 0, 2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-1, 1, 0, 0], [2, 0, 0, 0], [0, 0, 0, 0], [-5, 0, 0, 1], [-1, 1, -1, 1], [0, 0, 0, 0], [0, -2, 0, 0], [0, -1, 0, 0], [0, 0, 0, 0], [-2, 2, -2, 2], [0, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, 0], [-2, 2, 2, -2], [0, 0, 0, 0], [0, 6, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [2, -2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [2, 0, 0, 4], [-5, 5, -1, 1], [0, 0, 0, 0], [0, 1, -1, 0], [0, 0, -4, 0], [0, 0, 0, 0], [-2, 2, 2, -2], [-2, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 4, -4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 2, -2, 0], [0, 0, 0, 0], [0, 0, -2, 2], [6, 0, 0, 2], [0, 0, 0, 0], [-2, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 2, 2, 0], [0, 2, 0, 0], [0, 0, 0, 0], [9, -9, 1, -1], [6, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [-12, 12, -2, 2], [0, 0, 0, 0], [0, 8, 2, 0], [0, -2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-5, 0, 0, 2], [0, 0, 0, 0], [2, 0, 0, 2], [2, -2, -4, 4], [0, 0, 0, 0], [0, 5, -1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-3, 3, -2, 2], [1, 0, 0, -1], [0, 0, 0, 0], [0, 0, 0, -4], [-2, 2, 0, 0], [0, 0, 0, 0], [0, -2, 2, 0], [0, 2, 2, 0], [0, 0, 0, 0], [-2, 2, 0, 0], [-12, 0, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [-1, 1, 0, 0], [0, 0, 0, 0], [0, 0, 4, 0], [0, 11, -6, 0], [0, 0, 0, 0], [-2, 2, -2, 2], [0, 0, 0, 0], [0, 0, 0, 0], [2, 0, 0, -2]]}