# Stored data for newform 1800.3.v.m, downloaded from the LMFDB on 25 April 2024.
{"label": "1800.3.v.m", "space_label": "1800.3.v", "level": 1800, "weight": 3, "hecke_orbit": 13, "hecke_orbit_code": 54044638687790856, "dim": 4, "is_polredabs": true, "nf_label": "4.0.2304.2", "trace_hash": 116472871940295488, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [25, -40, 32, -8, 1]], [11, [-20, -4, 1]], [17, [16, -32, 32, 8, 1]]], "qexp_display": "q+(2-2\\beta _{2}+\\beta _{3})q^{7}+(2-2\\beta _{1}+2\\beta _{3})q^{11}+\\cdots", "char_order": 4, "char_parity": -1, "char_degree": 2, "char_conductor": 5, "char_orbit_label": "v", "char_is_real": false, "Nk2": 16200, "analytic_conductor": 49.04644758485344, "hecke_ring_index": 1, "level_radical": 30, "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": "0.250", "prec": 17}, "analytic_rank_proved": true, "char_values": [1800, 4, [1351, 901, 1001, 577], [4, 4, 4, 3]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [793, 1657], "field_disc": 2304, "field_disc_factorization": [[2, 8], [3, 2]], "field_poly": [9, 0, 0, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.069", "prec": 17}, {"__RealLiteral__": 0, "data": "3.901", "prec": 17}, {"__RealLiteral__": 0, "data": "1.661", "prec": 17}, {"__RealLiteral__": 0, "data": "52.321", "prec": 20}, {"__RealLiteral__": 0, "data": "43.188", "prec": 20}, {"__RealLiteral__": 0, "data": "1055.133", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c4", "trace_display": [0, 0, 0, 8], "traces": [0, 4, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 48, 0, 0, 0, -8, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 112, 0, 0, 0, 32, 0, 104, 0, 0, 0, -80, 0, 0, 0, 0, 0, -104, 0, 0, 0, 0, 0, 0, 0, -180, 0, 0, 0, 0, 0, 264, 0, 0, 0, -256, 0, 112, 0, 0, 0, 40, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 252, 0, 0, 0, 0, 0, 320, 0, 0, 0, 496, 0, 144, 0, 0, 0, 264, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, -372, 0, 0, 0, 0, 0, 208, 0, 0, 0, -320, 0, -64, 0, 0, 0, 240, 0, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, 0, 0, 572, 0, 0, 0, 0, 0, -32, 0, 0, 0, -216, 0, -248, 0, 0, 0, 328, 0, 0, 0, 0, 0, 456, 0, 0, 0, 0, 0, 0, 0, -412, 0, 0, 0, 0, 0, 32, 0, 0, 0, 424, 0, -272, 0, 0, 0, 240, 0, 0, 0, 0, 0, 184, 0, 0, 0, 0, 0, 0, 0, -92, 0, 0, 0, 0, 0, 160, 0, 0, 0, -72, 0, -456, 0, 0, 0, 328, 0, 0, 0, 0, 0, 872, 0, 0, 0, 0, 0, 0, 0, 796, 0, 0, 0, 0, 0, 360, 0, 0, 0, 320, 0, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, 264, 0, 0, 0, 0, 0, 0, 0, -632, 0, 0, 0, 0, 0, 464, 0, 0, 0, -1320, 0, 168, 0, 0, 0, 40, 0, 0, 0, 0, 0, -928, 0, 0, 0, 0, 0, 0, 0, 188, 0, 0, 0, 0, 0, -56, 0, 0, 0, 1192, 0, 336, 0, 0, 0, 64, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -1400, 0, 0, 0, 0, 0, -144, 0, 0, 0, 376, 0, 648, 0, 0, 0, -944, 0, 0, 0, 0, 0, -1256, 0, 0, 0, 0, 0, 0, 0, 1248, 0, 0, 0, 0, 0, -168, 0, 0, 0, -800, 0, -16, 0, 0, 0, -936, 0, 0, 0, 0, 0, -1104, 0, 0, 0, 0, 0, 0, 0, 432, 0, 0, 0, 0, 0, 48, 0, 0, 0, -1440, 0, 888, 0, 0, 0, -64, 0, 0, 0, 0, 0, 400, 0, 0, 0, 0, 0, 0, 0, -1208, 0, 0, 0, 0, 0, -72, 0, 0, 0, 2216, 0, 720, 0, 0, 0, -216, 0, 0, 0, 0, 0, -976, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -832, 0, 0, 0, -512, 0, 336, 0, 0, 0, -1256, 0, 0, 0, 0, 0, -248, 0, 0, 0, 0, 0, 0, 0, 1968, 0, 0, 0, 0, 0, -264, 0, 0, 0, 112, 0, 320, 0, 0, 0, -680, 0, 0, 0, 0, 0, 744, 0, 0, 0, 0, 0, 0, 0, 688, 0, 0, 0, 0, 0, -496, 0, 0, 0, -216, 0, -1560, 0, 0, 0, 56, 0, 0, 0, 0, 0, 264, 0, 0, 0, 0, 0, 0, 0, -500, 0, 0, 0, 0, 0, -1104, 0, 0, 0, 712, 0, -576, 0, 0, 0, -1008, 0, 0, 0, 0, 0, -472, 0, 0, 0, 0, 0, 0, 0, -1324, 0, 0, 0, 0, 0, -1216, 0, 0, 0, 904, 0, -976, 0, 0, 0, 680, 0, 0, 0, 0, 0, 1032, 0, 0, 0, 0, 0, 0, 0, -1612, 0, 0, 0, 0, 0, -2144, 0, 0, 0, -2760, 0, -672, 0, 0, 0, 696, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 404, 0, 0, 0, 0, 0, -1584, 0, 0, 0, 208, 0, -560, 0, 0, 0, -432, 0, 0, 0, 0, 0, -864, 0, 0, 0, 0, 0, 0, 0, -472, 0, 0, 0, 0, 0, -864, 0, 0, 0, 792, 0, -1968, 0, 0, 0, -72, 0, 0, 0, 0, 0, 2832, 0, 0, 0, 0, 0, 0, 0, 2088, 0, 0, 0, 0, 0, -112, 0, 0, 0, -184, 0, -272, 0, 0, 0, 1352, 0, 0, 0, 0, 0, -360, 0, 0, 0, 0, 0, 0, 0, 672, 0, 0, 0, 0, 0, 216, 0, 0, 0, -872, 0, -480, 0, 0, 0, 888, 0, 0, 0, 0, 0, -656, 0, 0, 0, 0, 0, 0, 0, -680, 0, 0, 0, 0, 0, -2112, 0, 0, 0, 1568, 0, 760, 0, 0, 0, -2016, 0, 0, 0, 0, 0, 2216, 0, 0, 0, 0, 0, 0, 0, -1184, 0, 0, 0, 0, 0, -824, 0, 0, 0, -1088, 0, -720, 0, 0, 0, 288, 0, 0, 0, 0, 0, 704, 0, 0, 0, 0, 0, 0, 0, -1700, 0, 0, 0, 0, 0, 64, 0, 0, 0, 3080, 0, -1272, 0, 0, 0, 1368, 0, 0, 0, 0, 0, -400, 0, 0, 0, 0, 0, 0, 0, -1356, 0, 0, 0, 0, 0, -648, 0, 0, 0, -4896, 0, -224, 0, 0, 0, -432, 0, 0, 0, 0, 0, 2032, 0, 0, 0, 0, 0, 0, 0, 7236, 0, 0, 0, 0, 0, 1536, 0, 0, 0, 704, 0, 296, 0, 0, 0, 352, 0, 0, 0, 0, 0, 736, 0, 0, 0, 0, 0, 0, 0, -352, 0, 0, 0, 0, 0, 1440, 0, 0, 0, 3784, 0, 1712, 0, 0, 0, -88, 0, 0, 0, 0, 0, -3912, 0, 0, 0, 0, 0, 0, 0, 568, 0, 0, 0, 0, 0, 1968, 0, 0, 0, 1128, 0, -720, 0, 0, 0, -1272, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, -2496, 0, 0, 0, 0, 0, 416, 0, 0, 0, -2552, 0, 1232, 0, 0, 0, -864, 0, 0, 0, 0, 0, -2368, 0, 0, 0, 0, 0, 0, 0, -1628, 0, 0, 0, 0, 0, 256, 0, 0, 0, 1560, 0, 752, 0, 0, 0, -1288, 0, 0, 0, 0, 0, -2288, 0, 0, 0, 0, 0, 0, 0, 524, 0, 0, 0, 0, 0, 3504, 0, 0, 0, -664, 0, 2448, 0, 0, 0, 936, 0, 0, 0, 0, 0, 784, 0, 0, 0, 0, 0, 0, 0, -2676, 0, 0, 0, 0, 0, 1360, 0, 0, 0, -1400, 0, 4200, 0, 0, 0, 1144, 0, 0, 0, 0, 0, -1792, 0, 0, 0, 0, 0, 0, 0, 1872, 0, 0, 0, 0, 0, 3592, 0, 0, 0, -5648, 0, 2416, 0, 0, 0, 336, 0, 0, 0, 0, 0, -2032, 0, 0, 0, 0, 0, 0, 0, 2432, 0, 0, 0, 0, 0, 3888, 0, 0, 0, 1576, 0, 1816, 0, 0, 0, 3024, 0, 0, 0, 0, 0, 480, 0, 0, 0, 0, 0, 0, 0, -1412, 0, 0, 0, 0, 0, 368, 0, 0, 0, 5784, 0, -528, 0, 0, 0, -336, 0, 0, 0, 0, 0, -536, 0, 0, 0, 0, 0, 0, 0, -2340, 0, 0, 0, 0, 0, 1968, 0, 0, 0, -1336, 0, 2992, 0, 0, 0, -3640, 0, 0, 0, 0, 0, -3040, 0, 0, 0, 0, 0, 0, 0, -968, 0, 0, 0, 0, 0, 176, 0, 0, 0, 1176, 0, 640, 0, 0, 0, 1280, 0, 0, 0, 0, 0, 3288, 0, 0, 0, 0, 0, 0, 0, -632, 0, 0, 0, 0, 0, 3904, 0, 0, 0, 32, 0, -1984, 0, 0, 0, 2984, 0, 0, 0, 0, 0, -1072, 0, 0, 0, 0, 0, 0, 0, 8940, 0, 0, 0, 0, 0, -488, 0, 0, 0, 64, 0, -1680, 0, 0, 0, 792, 0, 0, 0, 0, 0, -456, 0, 0, 0, 0, 0, 0, 0, -7396, 0, 0, 0, 0, 0, -576, 0, 0, 0, -5384, 0, -2712, 0, 0, 0, -1056, 0, 0, 0, 0, 0, 7752, 0, 0, 0, 0, 0, 0, 0, -632, 0, 0, 0, 0, 0, 4920, 0, 0, 0, -1328, 0, -224, 0, 0, 0, 1496, 0, 0, 0, 0, 0, 720, 0, 0, 0, 0, 0, 0, 0, -1028, 0, 0, 0, 0, 0, -2160, 0, 0, 0, -1832, 0, -2512, 0, 0, 0, 1800, 0, 0, 0, 0, 0, -4680, 0, 0, 0, 0, 0, 0, 0, 5884, 0, 0, 0, 0, 0, 1040, 0, 0, 0, 9936, 0, 0, 0, 0, 0, 704, 0, 0, 0, 0, 0, 4968, 0, 0, 0, 0, 0, 0, 0, 1616, 0, 0, 0, 0, 0, -3984, 0, 0, 0, 1040, 0, -1104, 0, 0, 0, 3608, 0, 0, 0, 0, 0, 2040, 0, 0, 0, 0, 0, 0, 0, 1568, 0, 0, 0, 0, 0, -1304, 0, 0, 0, 2136, 0, -4016, 0, 0, 0, -1888, 0, 0, 0, 0, 0, -440, 0, 0, 0, 0, 0, 0, 0, -1884, 0, 0, 0, 0, 0, 416, 0, 0, 0, -744, 0, 3312, 0, 0, 0, 5088, 0, 0, 0, 0, 0, 7448, 0, 0, 0, 0, 0, 0, 0, -1368, 0, 0, 0, 0, 0, -1584, 0, 0, 0, 2768, 0, 896, 0, 0, 0, 1184, 0, 0, 0, 0, 0, -536, 0, 0, 0, 0, 0, 0, 0, -8052, 0, 0, 0, 0, 0, 5584, 0, 0, 0, -8424, 0, -1480, 0, 0, 0, 24, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, -684, 0, 0, 0, 0, 0, -2872, 0, 0, 0, -7944, 0, -3984, 0, 0, 0, 1760, 0, 0, 0, 0, 0, 2960, 0, 0, 0, 0, 0, 0, 0, 8560, 0, 0, 0, 0, 0, -4000, 0, 0, 0, 1880, 0, -1176, 0, 0, 0, -7264, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 4676, 0, 0, 0, 0, 0, -1104, 0, 0, 0, 2720, 0, 3600, 0, 0, 0, 904, 0, 0, 0, 0, 0, -3448, 0, 0, 0, 0, 0, 0, 0, 5712, 0, 0, 0, 0, 0, -832, 0, 0, 0, 2008, 0, -1304, 0, 0, 0, 3160, 0, 0, 0, 0, 0, -904, 0, 0, 0, 0, 0, 0, 0, -6372, 0, 0, 0, 0, 0, 1976, 0, 0, 0, 784, 0, -1680, 0, 0, 0, 3568, 0, 0, 0, 0, 0, -1080, 0, 0, 0, 0, 0, 0, 0, -10768, 0, 0, 0, 0, 0, -272, 0, 0, 0, 4672, 0, -1440, 0, 0, 0, -2248, 0, 0, 0, 0, 0, -1344, 0, 0, 0, 0, 0, 0, 0, -1852, 0, 0, 0, 0, 0, -1488, 0, 0, 0, -384, 0, -96, 0, 0, 0, 64, 0, 0, 0, 0, 0, 1288, 0, 0, 0, 0, 0, 0, 0, -720, 0, 0, 0, 0, 0, -2784, 0, 0, 0, 600, 0, -376, 0, 0, 0, -960, 0, 0, 0, 0, 0, -1336, 0, 0, 0, 0, 0, 0, 0, 2524, 0, 0, 0, 0, 0, -6144, 0, 0, 0, -10032, 0, 4832, 0, 0, 0, -5904, 0, 0, 0, 0, 0, -4264, 0, 0, 0, 0, 0, 0, 0, 5304, 0, 0, 0, 0, 0, 368, 0, 0, 0, 2592, 0, -2104, 0, 0, 0, -2712, 0, 0, 0, 0, 0, 968, 0, 0, 0, 0, 0, 0, 0, -5580, 0, 0, 0, 0, 0, 3224, 0, 0, 0, 632, 0, -4000, 0, 0, 0, 920, 0, 0, 0, 0, 0, 3464, 0, 0, 0, 0, 0, 0, 0, 1476, 0, 0, 0, 0, 0, -976, 0, 0, 0, 3736, 0, -384, 0, 0, 0, 96, 0, 0, 0, 0, 0, -2608, 0, 0, 0, 0, 0, 0, 0, -1792, 0, 0, 0, 0, 0, -304, 0, 0, 0, 16, 0, 3424, 0, 0, 0, -4992, 0, 0, 0, 0, 0, 3048, 0, 0, 0, 0, 0, 0, 0, 7076, 0, 0, 0, 0, 0, 912, 0, 0, 0, -1216, 0, 7944, 0, 0, 0, -2616, 0, 0, 0, 0, 0, -6488, 0, 0, 0, 0, 0, 0, 0, 1812, 0, 0, 0, 0, 0, -672, 0, 0, 0, 520, 0, -5088, 0, 0, 0, -5264, 0, 0, 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, 5, 3, -1, 4, 0]], "char_orbit_index": 22, "prim_orbit_index": 3, "minimal_twist": "600.3.u.c", "char_is_minimal": true, "conrey_index": 793, "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], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [2, 0, -2, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [2, -2, 0, 2], [0, 0, 0, 0], [12, -5, 12, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-2, 0, 2, 2], [0, 0, 0, 0], [0, 2, -5, 2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-18, -6, -18, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -14, 2, -14], [0, 0, 0, 0], [11, -6, 0, 6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [28, 0, -28, -12], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [8, 2, 0, -2], [0, 0, 0, 0], [26, 19, 26, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-20, 0, 20, -14], [0, 0, 0, 0], [0, 4, 38, 4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-26, 32, -26, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -32, 2, -32], [0, 0, 0, 0], [-45, -24, 0, 24], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [66, 0, -66, 15], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-64, 14, 0, -14], [0, 0, 0, 0], [28, -20, 28, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [10, 0, -10, 10], [0, 0, 0, 0], [0, -4, -78, -4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [4, -70, 4, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -28, -28, -28], [0, 0, 0, 0], [63, -22, 0, 22], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [80, 0, -80, 21], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}