# Stored data for newform 2268.2.i.k, downloaded from the LMFDB on 18 April 2024.
{"label": "2268.2.i.k", "space_label": "2268.2.i", "level": 2268, "weight": 2, "hecke_orbit": 11, "hecke_orbit_code": 45036546063075548, "dim": 6, "is_polredabs": true, "nf_label": "6.0.309123.1", "trace_hash": 1032291911115787480, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [81, 108, 135, 30, 13, -1, 1]], [13, [441, -231, 163, -20, 15, -2, 1]], [19, [2401, 1764, 1443, -10, 45, 3, 1]]], "qexp_display": "q+(-\\beta _{1}-\\beta _{2}-\\beta _{4}+\\beta _{5})q^{5}+(1+\\beta _{3}+\\cdots)q^{7}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 63, "char_orbit_label": "i", "char_is_real": false, "Nk2": 9072, "analytic_conductor": 18.11007117842639, "hecke_ring_index": 9, "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": "0.009", "prec": 17}, "analytic_rank_proved": true, "char_values": [2268, 3, [1135, 1541, 325], [3, 2, 2]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [865, 2053], "field_disc": -309123, "field_disc_factorization": [[-1, 1], [3, 3], [107, 2]], "field_poly": [3, -12, 19, -15, 10, -3, 1], "hecke_ring_index_factorization": [[3, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.783", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "127.661", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5002.063", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c3", "trace_display": [0, 0, 1, 2], "traces": [0, 6, 0, 0, 0, 1, 0, 2, 0, 0, 0, 5, 0, 2, 0, 0, 0, -4, 0, -3, 0, 0, 0, 14, 0, -10, 0, 0, 0, -5, 0, -4, 0, 0, 0, 26, 0, 0, 0, 0, 0, 12, 0, 9, 0, 0, 0, 18, 0, 12, 0, 0, 0, 6, 0, 16, 0, 0, 0, 10, 0, 14, 0, 0, 0, -48, 0, -32, 0, 0, 0, -22, 0, 1, 0, 0, 0, -44, 0, -16, 0, 0, 0, 17, 0, -5, 0, 0, 0, -3, 0, 5, 0, 0, 0, -64, 0, -14, 0, 0, 0, -29, 0, 21, 0, 0, 0, 39, 0, 4, 0, 0, 0, 13, 0, -23, 0, 0, 0, 1, 0, -16, 0, 0, 0, -108, 0, 2, 0, 0, 0, -20, 0, 49, 0, 0, 0, 28, 0, 40, 0, 0, 0, 3, 0, 8, 0, 0, 0, 21, 0, -26, 0, 0, 0, 24, 0, -30, 0, 0, 0, 37, 0, 3, 0, 0, 0, 28, 0, 13, 0, 0, 0, 46, 0, 60, 0, 0, 0, 21, 0, 20, 0, 0, 0, 86, 0, 68, 0, 0, 0, -90, 0, -72, 0, 0, 0, 38, 0, 21, 0, 0, 0, -13, 0, -54, 0, 0, 0, 52, 0, -30, 0, 0, 0, -46, 0, 17, 0, 0, 0, -18, 0, -48, 0, 0, 0, 9, 0, 25, 0, 0, 0, 35, 0, -9, 0, 0, 0, 24, 0, 9, 0, 0, 0, 31, 0, -29, 0, 0, 0, -24, 0, -22, 0, 0, 0, 3, 0, 28, 0, 0, 0, 39, 0, 72, 0, 0, 0, -59, 0, -28, 0, 0, 0, 70, 0, -45, 0, 0, 0, -1, 0, 4, 0, 0, 0, 39, 0, 5, 0, 0, 0, 27, 0, 20, 0, 0, 0, -18, 0, 55, 0, 0, 0, 39, 0, -2, 0, 0, 0, -32, 0, 22, 0, 0, 0, -24, 0, -98, 0, 0, 0, -86, 0, -49, 0, 0, 0, -81, 0, 18, 0, 0, 0, 13, 0, -34, 0, 0, 0, 3, 0, -61, 0, 0, 0, -60, 0, -41, 0, 0, 0, -21, 0, 64, 0, 0, 0, 43, 0, -24, 0, 0, 0, -56, 0, -12, 0, 0, 0, -66, 0, -38, 0, 0, 0, 6, 0, 10, 0, 0, 0, -19, 0, 113, 0, 0, 0, -29, 0, 53, 0, 0, 0, 3, 0, -19, 0, 0, 0, 6, 0, -26, 0, 0, 0, 28, 0, -36, 0, 0, 0, 56, 0, 19, 0, 0, 0, 33, 0, 2, 0, 0, 0, -80, 0, 110, 0, 0, 0, 18, 0, 66, 0, 0, 0, 4, 0, 74, 0, 0, 0, -106, 0, -174, 0, 0, 0, 106, 0, 27, 0, 0, 0, 0, 0, -140, 0, 0, 0, 10, 0, 16, 0, 0, 0, -17, 0, 42, 0, 0, 0, -26, 0, -119, 0, 0, 0, 8, 0, 43, 0, 0, 0, -32, 0, -6, 0, 0, 0, 51, 0, 34, 0, 0, 0, 82, 0, -2, 0, 0, 0, -6, 0, -94, 0, 0, 0, -15, 0, 57, 0, 0, 0, -7, 0, 90, 0, 0, 0, -21, 0, 42, 0, 0, 0, 9, 0, -49, 0, 0, 0, -39, 0, -36, 0, 0, 0, -46, 0, 2, 0, 0, 0, -14, 0, 29, 0, 0, 0, 104, 0, 116, 0, 0, 0, -23, 0, -74, 0, 0, 0, -22, 0, 206, 0, 0, 0, 114, 0, -64, 0, 0, 0, -98, 0, -41, 0, 0, 0, -2, 0, -18, 0, 0, 0, -58, 0, -29, 0, 0, 0, 60, 0, -31, 0, 0, 0, 30, 0, -54, 0, 0, 0, -13, 0, 44, 0, 0, 0, 18, 0, -37, 0, 0, 0, -34, 0, -83, 0, 0, 0, -54, 0, -73, 0, 0, 0, -56, 0, 6, 0, 0, 0, 6, 0, 113, 0, 0, 0, 32, 0, 78, 0, 0, 0, 75, 0, -26, 0, 0, 0, -51, 0, -49, 0, 0, 0, 23, 0, -2, 0, 0, 0, -113, 0, -11, 0, 0, 0, -57, 0, -30, 0, 0, 0, 30, 0, 18, 0, 0, 0, -27, 0, 92, 0, 0, 0, 156, 0, 60, 0, 0, 0, 76, 0, -126, 0, 0, 0, 52, 0, 15, 0, 0, 0, 107, 0, -90, 0, 0, 0, 9, 0, -87, 0, 0, 0, 18, 0, 28, 0, 0, 0, 140, 0, -83, 0, 0, 0, 40, 0, 62, 0, 0, 0, -61, 0, -49, 0, 0, 0, 84, 0, 48, 0, 0, 0, 21, 0, -22, 0, 0, 0, 94, 0, 38, 0, 0, 0, 41, 0, 18, 0, 0, 0, -15, 0, 55, 0, 0, 0, 52, 0, -49, 0, 0, 0, -66, 0, -40, 0, 0, 0, -79, 0, -130, 0, 0, 0, -34, 0, -32, 0, 0, 0, 12, 0, 63, 0, 0, 0, 110, 0, 122, 0, 0, 0, -23, 0, -20, 0, 0, 0, -184, 0, -48, 0, 0, 0, 134, 0, -98, 0, 0, 0, -66, 0, -41, 0, 0, 0, 47, 0, 20, 0, 0, 0, -19, 0, 38, 0, 0, 0, 2, 0, -3, 0, 0, 0, 142, 0, 0, 0, 0, 0, -39, 0, 0, 0, 0, 0, -44, 0, 38, 0, 0, 0, -129, 0, -29, 0, 0, 0, -75, 0, -2, 0, 0, 0, 144, 0, 12, 0, 0, 0, 12, 0, 122, 0, 0, 0, -72, 0, 129, 0, 0, 0, -3, 0, 27, 0, 0, 0, -120, 0, -40, 0, 0, 0, 51, 0, 44, 0, 0, 0, 29, 0, 121, 0, 0, 0, -75, 0, 58, 0, 0, 0, -276, 0, 159, 0, 0, 0, -26, 0, 126, 0, 0, 0, -134, 0, 144, 0, 0, 0, -8, 0, -110, 0, 0, 0, -70, 0, 90, 0, 0, 0, 50, 0, -134, 0, 0, 0, -67, 0, -33, 0, 0, 0, 45, 0, -33, 0, 0, 0, -60, 0, -51, 0, 0, 0, 87, 0, 31, 0, 0, 0, -113, 0, 39, 0, 0, 0, -7, 0, -12, 0, 0, 0, 90, 0, -41, 0, 0, 0, 174, 0, -72, 0, 0, 0, 9, 0, 10, 0, 0, 0, -56, 0, 4, 0, 0, 0, -69, 0, -11, 0, 0, 0, 30, 0, -109, 0, 0, 0, -78, 0, 2, 0, 0, 0, -27, 0, -85, 0, 0, 0, -62, 0, 41, 0, 0, 0, -58, 0, -36, 0, 0, 0, -85, 0, -12, 0, 0, 0, -184, 0, -96, 0, 0, 0, 56, 0, -176, 0, 0, 0, 72, 0, -45, 0, 0, 0, 63, 0, 74, 0, 0, 0, -55, 0, -86, 0, 0, 0, 34, 0, -65, 0, 0, 0, 22, 0, -15, 0, 0, 0, -39, 0, 136, 0, 0, 0, -58, 0, 38, 0, 0, 0, 11, 0, -72, 0, 0, 0, -16, 0, -73, 0, 0, 0, 70, 0, 192, 0, 0, 0, -13, 0, 139, 0, 0, 0, -14, 0, 43, 0, 0, 0, 45, 0, -29, 0, 0, 0, -84, 0, 25, 0, 0, 0, 63, 0, -50, 0, 0, 0, -175, 0, 40, 0, 0, 0, -81, 0, -18, 0, 0, 0, 26, 0, 11, 0, 0, 0, 24, 0, 54, 0, 0, 0, -4, 0, 78, 0, 0, 0, 176, 0, -72, 0, 0, 0, 302, 0, -7, 0, 0, 0, 155, 0, -92, 0, 0, 0, -69, 0, 27, 0, 0, 0, -9, 0, 236, 0, 0, 0, 288, 0, -64, 0, 0, 0, 102, 0, 18, 0, 0, 0, -52, 0, -47, 0, 0, 0, -13, 0, 65, 0, 0, 0, -108, 0, 15, 0, 0, 0, 96, 0, -92, 0, 0, 0, 145, 0, -85, 0, 0, 0, -39, 0, 32, 0, 0, 0, 18, 0, 45, 0, 0, 0, 48, 0, -87, 0, 0, 0, -42, 0, 54, 0, 0, 0, -56, 0, -39, 0, 0, 0, 46, 0, 44, 0, 0, 0, -56, 0, 73, 0, 0, 0, -18, 0, -36, 0, 0, 0, 162, 0, 258, 0, 0, 0, 294, 0, 52, 0, 0, 0, -12, 0, 37, 0, 0, 0, 9, 0, 28, 0, 0, 0, -105, 0, 26, 0, 0, 0, -35, 0, -182, 0, 0, 0, 18, 0, 76, 0, 0, 0, 47, 0, -90, 0, 0, 0, 5, 0, -3, 0, 0, 0, 2, 0, -156, 0, 0, 0, 31, 0, 10, 0, 0, 0, 56, 0, -220, 0, 0, 0, -57, 0, 28, 0, 0, 0, -114, 0, 4, 0, 0, 0, 138, 0, -80, 0, 0, 0, -99, 0, 29, 0, 0, 0, 31, 0, -20, 0, 0, 0, -47, 0, 61, 0, 0, 0, -27, 0, -96, 0, 0, 0, -40, 0, -18, 0, 0, 0, -17, 0, 40, 0, 0, 0, 116, 0, -82, 0, 0, 0, 66, 0, 20, 0, 0, 0, -36, 0, 115, 0, 0, 0, 137, 0, -168, 0, 0, 0, 90, 0, -53, 0, 0, 0, -19, 0, 142, 0, 0, 0, -192, 0, -39, 0, 0, 0, 45, 0, 16, 0, 0, 0, 27, 0, -96, 0, 0, 0, -18, 0, 118, 0, 0, 0, 178, 0, 22, 0, 0, 0, -128, 0, 120, 0, 0, 0, 15, 0, -82, 0, 0, 0, 71, 0, -28, 0, 0, 0, -73, 0, 60, 0, 0, 0, -56, 0, -9, 0, 0, 0, -22, 0, -210, 0, 0, 0, -93, 0, -70, 0, 0, 0, -115, 0, 44, 0, 0, 0, -222, 0, 10, 0, 0, 0, -119, 0, 74, 0, 0, 0, -34, 0, -58, 0, 0, 0, 28, 0, -60, 0, 0, 0, -210, 0, -102, 0, 0, 0, -147, 0, 228, 0, 0, 0, 2, 0, 55, 0, 0, 0, 45, 0, 39, 0, 0, 0, -78, 0, 37, 0, 0, 0, 2, 0, 11, 0, 0, 0, -49, 0, 93, 0, 0, 0, 69, 0, -16, 0, 0, 0, -92, 0, 38, 0, 0, 0, 52, 0, 276, 0, 0, 0, -78, 0, 117, 0, 0, 0, 50, 0, -5, 0, 0, 0, 53, 0, 66, 0, 0, 0, -10, 0, 7, 0, 0, 0, 37, 0, 178, 0, 0, 0, -63, 0, 51, 0, 0, 0, -7, 0, -3, 0, 0, 0, 114, 0, -44, 0, 0, 0, -33, 0, -2, 0, 0, 0, 0, 0, 130, 0, 0, 0, -138, 0, 174, 0, 0, 0, 294, 0, 26, 0, 0, 0, -88, 0, -98, 0, 0, 0, -5, 0, -11, 0, 0, 0, -44, 0, -131, 0, 0, 0, 186, 0, -48, 0, 0, 0, -99, 0, -34, 0, 0, 0, 13, 0, -24, 0, 0, 0, 28, 0, 26, 0, 0, 0, -111, 0, -105, 0, 0, 0, 42, 0, -210, 0, 0, 0, 57, 0, -53, 0, 0, 0, -77, 0, 4, 0, 0, 0, 18, 0, -97, 0, 0, 0, -58, 0, 20, 0, 0, 0, 136, 0, 140, 0, 0, 0, 90, 0, -20, 0, 0, 0, 168, 0, -2, 0, 0, 0, 18, 0, -144, 0, 0, 0, 84, 0, -198, 0, 0, 0, -252, 0, -336, 0, 0, 0, 30, 0, 104, 0, 0, 0, 68, 0, -203, 0, 0, 0, 21, 0, 92, 0, 0, 0, -24, 0, -12, 0, 0, 0, -76, 0, -189, 0, 0, 0, -38, 0, 33, 0, 0, 0, -86, 0, -13, 0, 0, 0, 17, 0, 53, 0, 0, 0, -82, 0, -27, 0, 0, 0, -85, 0, 87, 0, 0, 0, -198, 0, 64, 0, 0, 0, -23, 0, 53, 0, 0, 0, 9, 0, -71, 0, 0, 0, -87, 0, -61, 0, 0, 0, 150, 0, 136, 0, 0, 0, -154, 0, 16, 0, 0, 0, 266, 0, -27, 0, 0, 0, -56, 0, 39, 0, 0, 0, 138, 0, 58, 0, 0, 0, 61, 0, 68, 0, 0, 0, 6, 0, -144, 0, 0, 0, -152, 0, -42, 0, 0, 0, -258, 0, 73, 0, 0, 0, 79, 0, -156, 0, 0, 0, 75, 0, 131, 0, 0, 0, 30, 0, 141, 0, 0, 0, -282, 0, -19, 0, 0, 0, -15, 0, -77, 0, 0, 0, -3, 0, -2, 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, 63, 8, 1, 3, 0]], "char_orbit_index": 9, "prim_orbit_index": 8, "minimal_twist": "756.2.k.e", "char_is_minimal": false, "conrey_index": 865, "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, 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], [0, -1, -1, 0, -1, 1], [0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 1, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [2, 1, 1, 1, 2, 0], [0, 0, 0, 0, 0, 0], [0, 0, -1, -1, 0, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -1, 0, -1, 1, 1], [0, 0, 0, 0, 0, 0], [-2, -1, -2, -2, -2, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, -1, 1, -5, 0], [0, 0, 0, 0, 0, 0], [-5, -1, -3, -3, -5, 2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 2, -1], [0, 0, 0, 0, 0, 0], [0, -1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [5, -2, 1, 1, -1, 0], [0, 0, 0, 0, 0, 0], [1, -1, 1, 1, 1, -2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [3, -1, -2, -2, 3, 1], [0, 0, 0, 0, 0, 0], [0, -1, -2, 1, -4, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [3, 1, 2, -1, 0, 2], [0, 0, 0, 0, 0, 0], [1, 3, 2, 0, 0, -2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 3, 3, 0, 0, -3], [0, 0, 0, 0, 0, 0], [5, -4, -1, 4, 0, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [2, -1, -1, 1, 0, -1], [0, 0, 0, 0, 0, 0], [3, -2, -2, 2, 0, -2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-9, 1, -1, -1, 0, -1], [0, 0, 0, 0, 0, 0], [-5, -1, -1, 1, 0, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-2, -3, -1, 3, 0, -1], [0, 0, 0, 0, 0, 0], [0, -3, -2, -1, -2, 3], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-7, 1, 3, 2, 0, -3], [0, 0, 0, 0, 0, 0], [-3, -1, -3, 1, 0, -3], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, 1, 0, -5, -1], [0, 0, 0, 0, 0, 0], [-2, 1, 0, 0, -2, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-3, 2, -2, -2, -3, 4], [0, 0, 0, 0, 0, 0], [-1, -3, -2, 0, -5, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-14, 5, 0, -5, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, -2, 2, 4, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]]}