# Stored data for newform 637.2.f.k, downloaded from the LMFDB on 29 March 2024. {"label": "637.2.f.k", "space_label": "637.2.f", "level": 637, "weight": 2, "hecke_orbit": 11, "hecke_orbit_code": 45036339904643709, "dim": 12, "is_polredabs": true, "trace_hash": 2251676033842330364, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [9, -42, 172, -178, 236, -86, 147, -48, 50, -10, 10, -2, 1]], [3, [1, 1, 7, 2, 33, 11, 55, -17, 47, -1, 8, -1, 1]], [5, [3, 17, 6, -18, -11, 1, 1]]], "qexp_display": "q+(-\\beta _{1}-\\beta _{5}+\\beta _{11})q^{2}+\\beta _{11}q^{3}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 13, "char_orbit_label": "f", "char_is_real": false, "Nk2": 2548, "analytic_conductor": 5.086470608755561, "hecke_ring_index": 1, "level_radical": 91, "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": "0.010", "prec": 17}, "analytic_rank_proved": true, "char_values": [637, 3, [248, 197], [3, 2]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [7, 13], "conrey_indexes": [295, 393], "field_disc": 35678280258076401, "field_disc_factorization": [[3, 6], [11, 2], [635983, 2]], "field_poly": [1, 1, 8, 1, 47, 17, 55, -11, 33, -2, 7, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.020", "prec": 17}, {"__RealLiteral__": 0, "data": "11.224", "prec": 20}, {"__RealLiteral__": 0, "data": "0.990", "prec": 17}, {"__RealLiteral__": 0, "data": "533.330", "prec": 24}, {"__RealLiteral__": 0, "data": "353.155", "prec": 24}, {"__RealLiteral__": 0, "data": "50108.634", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.3.c3", "trace_display": [2, 1, -2, 0], "traces": [0, 12, 2, 1, -4, -2, -9, 0, -6, 3, 4, 4, -10, -2, 0, -2, 8, 5, -6, -1, -1, 0, -5, -1, -11, -14, 11, -8, 0, 3, -5, -32, 8, 16, 32, 0, -21, -13, 34, 43, 10, -8, 0, -11, -42, -7, 16, 2, 21, 0, 6, 40, -16, 4, -18, 9, 0, 42, -8, 13, -40, -5, 5, 0, -30, -14, -36, -11, 29, 23, 0, 6, 25, 60, -3, -3, -9, 0, 16, -14, -7, -6, 1, -54, 0, -1, 14, 16, 0, 4, -16, 0, 54, -7, 45, -6, -38, -35, 0, -20, 40, 31, 38, -54, -48, 0, -9, 45, 27, 2, 8, 12, 0, -21, 30, -51, -50, 14, -12, 0, -19, 8, -130, -3, -10, 60, 0, -6, -52, -16, 12, -52, 2, 0, -2, -60, -33, -25, 64, 21, 0, 5, -10, -50, 38, 25, 52, 0, 50, -32, 46, -38, 5, 28, 0, -58, -73, -20, 10, 6, 16, 0, 23, 19, 84, -17, -24, -23, 0, 36, 16, 32, -43, 31, -132, 0, -43, 20, 71, -4, -27, 58, 0, -66, 34, 69, 21, 10, 27, 0, -6, 31, -28, 8, 42, 26, 0, 25, 44, 5, 98, -11, 36, 0, -68, 19, -63, 60, -23, -68, 0, -30, -1, -86, -15, 9, 12, 0, 2, -11, 64, -4, 46, 5, 0, 32, -178, -34, -27, 48, 59, 0, -1, 118, -87, 12, -36, 50, 0, 124, -7, 50, 38, 3, 13, 0, 88, -73, 4, -16, -11, -7, 0, -3, 71, 48, -18, 45, -62, 0, 56, -120, -3, -24, 2, -106, 0, 10, 128, 73, -13, -49, -12, 0, 30, -28, 124, -6, -56, -11, 0, -42, 89, 46, 32, -16, -47, 0, -2, 53, -4, 50, -31, 60, 0, -46, 40, -51, -36, -82, 42, 0, -108, 30, -176, 22, -76, -8, 0, 4, -57, -72, -91, -42, 19, 0, -2, -90, -33, -65, 44, -30, 0, -12, -24, -80, -68, 81, 38, 0, -10, -40, 37, -6, 23, 23, 0, -80, -55, -52, 25, 29, -35, 0, 58, 26, 82, 2, -18, -61, 0, -20, -34, -28, -75, 21, -108, 0, -95, 48, 43, -15, -4, 78, 0, 48, 35, 46, -15, 56, -41, 0, 66, 56, 28, -23, 134, -96, 0, -11, 67, 3, 188, 19, 52, 0, 16, -40, -69, 110, 4, -100, 0, -16, 18, -122, -4, 102, 126, 0, -51, -54, 214, 63, -48, -2, 0, -2, -146, -41, -15, -4, 73, 0, 138, 84, -55, 62, -42, 83, 0, 76, -85, 91, -32, -43, -14, 0, -40, 1, -34, 13, -15, -2, 0, -22, 10, 76, -35, 35, 7, 0, 81, 36, -20, -39, 4, 38, 0, 1, 78, 49, -7, -56, 140, 0, -52, -26, 104, -24, -48, 66, 0, 40, 2, 26, 8, -78, -75, 0, -33, 55, 20, -40, 24, 29, 0, -29, 78, -53, -64, -81, -78, 0, 15, 1, -252, 39, -45, -20, 0, 64, 17, 18, 49, 26, 11, 0, -15, -192, 32, 21, 50, 52, 0, 13, 62, -8, 52, -59, 49, 0, -24, 19, -49, -32, 50, 8, 0, -76, -51, -56, 30, 21, -22, 0, 29, 3, 94, -75, -36, -101, 0, -26, -124, 43, 55, -93, -40, 0, -32, 72, 88, -24, 43, -44, 0, 42, 2, 45, -1, 84, -125, 0, -180, 12, 1, 39, 114, -1, 0, 20, 66, 19, 22, -43, -56, 0, 6, -2, 12, 50, 30, 140, 0, -13, 60, -50, 69, 83, 6, 0, -125, -20, 64, 14, 98, 18, 0, -1, -34, -16, 44, -72, 13, 0, 10, -48, -73, -126, 28, -6, 0, 170, 55, 63, -166, -14, -6, 0, 98, 35, -182, -43, 92, 34, 0, -58, 93, 28, -7, 71, -63, 0, -9, -8, -39, -1, -55, -74, 0, 79, -84, -56, 35, -2, 80, 0, 168, -26, -17, -82, -296, -66, 0, -64, 59, 98, -20, -124, -123, 0, -61, 7, -6, -38, 58, 25, 0, 4, 6, -73, -248, 72, 58, 0, 10, -2, -114, 58, -21, 28, 0, 16, -106, 12, 119, -152, -48, 0, -41, 56, -28, -57, -208, -32, 0, 39, -90, -41, 100, 139, 83, 0, -60, -55, 21, -78, 65, 33, 0, -188, -97, -16, -24, -28, 80, 0, 62, -40, -22, 10, -115, 93, 0, 15, -86, 99, 35, 84, -16, 0, -40, 40, 22, -17, 37, -12, 0, -150, -9, 51, 31, 60, 113, 0, 2, 84, 9, -25, 132, -36, 0, 38, 49, 16, -28, -69, -13, 0, 68, 26, -13, 40, 53, -202, 0, 45, -38, 180, -62, 56, 34, 0, 31, 51, 184, -23, 212, 5, 0, -42, 148, -23, 80, -88, 65, 0, 43, 66, 5, 226, -98, -74, 0, 130, -6, 47, 162, -21, -28, 0, 86, -8, 144, -1, -61, -10, 0, -22, 33, -108, 0, 105, 19, 0, 23, 216, -30, 17, 0, 20, 0, 85, 78, 5, -29, -32, -46, 0, 20, 30, -123, 56, 12, -39, 0, -4, -135, 39, 23, -142, -16, 0, -27, -20, -41, 14, 0, -59, 0, 9, -17, 36, -60, -11, 182, 0, -24, -109, -166, 125, 33, 2, 0, 24, -35, -116, 78, 18, -25, 0, -102, -182, 20, 51, -20, 94, 0, -88, -18, 19, -138, -55, -109, 0, -66, 62, -126, 12, 60, 68, 0, -134, 161, -98, 16, 94, 7, 0, -26, -19, 134, -15, -94, -20, 0, 28, -84, 11, 40, 7, 20, 0, -56, -38, 125, -36, 143, -42, 0, 86, -49, -29, -52, 36, -74, 0, -148, -61, -57, 87, 244, 159, 0, 122, -51, 39, 62, 22, -3, 0, -8, -37, 73, -30, -29, 144, 0, -21, 64, 130, -195, 20, 50, 0, 15, 10, -82, -20, -144, 134, 0, 91, 20, -56, -42, 108, -113, 0, -29, -60, 69, -116, -20, 15, 0, -42, -35, 56, -60, 33, -61, 0, 314, -141, 158, -95, -74, -3, 0, -4, -60, -150, -25, 80, 83, 0, 96, 92, -44, 1, -112, -206, 0, 78, 54, -74, 26, -59, 88], "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, 13, 3, 1, 3, 0]], "char_orbit_index": 6, "prim_orbit_index": 3, "minimal_twist": "91.2.g.b", "char_is_minimal": true, "conrey_index": 295, "id": null, "nf_label": 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, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, -2, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0], [1, 1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 0], [1, -1, 0, 0, 0, -1, 0, -1, 0, 0, -1, -1], [-1, 0, 1, 2, 0, 0, 1, 0, 0, -1, 1, -2], [0, -1, 0, -1, 1, 0, -1, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [2, 1, 0, 0, 1, 1, 0, -2, 1, 0, -1, -2], [0, 0, 0, -1, 0, 0, -1, 1, 0, 0, 0, 0], [-1, 0, 1, 2, 0, -2, 1, 0, 0, -1, 1, -2], [0, 2, 1, -2, 0, 0, 1, -1, 2, 0, 0, 0], [0, 0, -1, 1, 0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0], [-1, -2, 0, 0, -1, -2, 0, 1, -1, -3, 1, -1], [-2, 0, 0, 0, 0, 0, 0, 2, 0, -1, 1, -2], [-2, 0, -1, -1, 0, -1, 2, 0, 0, 1, 2, 1], [2, -2, 0, 0, -2, -2, -1, -1, 0, -1, -2, 0], [-1, 0, 1, 0, 0, 1, 1, 0, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 0, 0, -2, -2, 0, -1, -2, 0, -1, -1], [0, 0, 0, 1, 0, 0, 1, -1, 0, 0, 0, 0], [-3, 0, 2, 0, 0, -2, -1, 0, 0, -2, -1, 0], [0, -2, -1, 2, 0, 0, 1, 2, 1, 0, 0, 0], [0, 0, 1, 2, 0, 0, 0, 3, 1, 0, 0, 0], [3, 0, 0, -2, -1, -1, -2, 0, 0, 0, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 0, 0, 2, 0, 0, 4, 2, -1, 1, -2], [-2, 0, 0, 0, 0, 0, 0, 2, 0, 3, 1, 0], [4, 0, -1, 0, 0, 4, -1, 0, 0, 1, -1, 0], [5, 1, 0, 0, -1, 1, -1, -1, 0, 1, -2, -1], [1, 0, -2, 1, 1, 1, 1, 0, 0, 2, 1, -1], [-2, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, -1, 0, 0, 2, -3, 0, 0, 0, 0], [-3, 0, -2, 0, 1, 2, 0, 0, 0, 2, 0, 0], [0, 0, -2, 1, 0, 0, 1, -1, 0, 0, 0, 0], [0, 0, -2, -1, 0, 0, -2, 4, 3, 0, 0, 0], [-2, 0, 0, -3, 2, -4, 2, 0, 0, 0, 2, 3], [0, 1, 1, 1, 0, 0, -1, 4, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 3, 0, 0, 0, 3, 0, -2, 0, 1, 1, -4], [4, 0, -1, -2, -1, 0, -2, 0, 0, 1, -2, 2], [1, -1, -1, 2, 0, 1, -1, -3, 0, 2, -1, 2], [0, 0, 3, 0, -2, -1, 0, 0, 0, -3, 0, 0], [-3, 0, 0, 0, -1, 0, 0, 3, -1, -1, 1, -2], [1, 1, 0, 0, -1, 1, 0, -1, -1, 0, 2, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 1, -2, -2, -2, 0, 0, 0, -1, 0, 2], [0, 3, 2, 4, 0, 0, 0, -1, 3, 0, 0, 0], [0, -1, 1, -1, 0, 0, 2, 1, -2, 0, 0, 0], [-3, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, -2], [0, -6, -2, 5, 0, 0, -2, 2, 0, 0, 0, 0], [1, 1, 0, 0, 2, 1, 0, -1, 2, -2, -1, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, -2, 2, 2, 3, 1, 0, 0, 2, 1, -2], [-1, 1, 3, -1, -2, 0, -1, -1, 0, -2, 1, 1], [-5, 0, 0, -4, 2, -2, 2, 0, 0, 0, 2, 4], [-3, 1, 0, 0, 2, 1, 0, 3, 2, 2, 3, 2], [5, -1, 0, 0, -1, -1, 0, -5, -1, 1, -2, 4], [0, -1, -1, 0, 0, 0, -5, 6, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 3, 0, 0, -2, 2, -2, 0, 0, 0], [0, 3, -1, -3, 0, 0, -1, 4, 2, 0, 0, 0], [4, 0, 0, -1, 0, -5, 0, 0, 0, 0, 0, 1], [0, 5, 3, -3, 0, 0, -1, -2, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, -4], [0, 1, 0, 0, 0, 1, 0, 0, 0, 3, -3, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 1, 2, 0, -2, 0, 0, 0, 1, -1, 6], [-2, 0, 2, -3, 1, 1, 0, 0, 0, -2, 0, 3], [-2, -1, 0, 0, -2, -1, 0, 2, -2, -1, 2, 1], [0, 0, 0, 0, -3, 0, 0, 0, -3, -1, -1, -2], [0, 3, 1, -4, 0, 0, -1, -1, -1, 0, 0, 0], [-4, 0, -1, 1, -3, 0, 1, 0, 0, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, -1, 0, 0, -1, 0, 1, 0, 0, 0], [2, 0, 0, 5, 1, 3, 1, 0, 0, 0, 1, -5], [0, -2, 1, 6, 0, 0, 0, 4, 1, 0, 0, 0], [0, 1, 0, 0, 2, 1, 0, 0, 2, 1, 0, 0], [4, 8, 0, 0, 1, 8, 0, -4, 1, 0, -4, -5], [-1, 0, -2, 2, 1, 3, 2, 0, 0, 2, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 1, -7, -3, 0, -1, 0, 0, -1, -1, 7], [-1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, -2], [8, -2, 0, 0, 1, -2, 0, -8, 1, -2, -1, -6], [0, -3, -2, 2, 0, 0, -4, 1, -3, 0, 0, 0], [-5, 0, 1, -3, 2, -1, 2, 0, 0, -1, 2, 3], [0, 2, 0, -4, 0, 0, 3, -8, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, -2, 2, -4, 0, 0, 0, 0, 0, 2], [0, 1, -1, -1, 0, 0, -1, 7, 1, 0, 0, 0]]}