# Stored data for newform 810.4.e.u, downloaded from the LMFDB on 29 March 2024. {"label": "810.4.e.u", "space_label": "810.4.e", "level": 810, "weight": 4, "hecke_orbit": 21, "hecke_orbit_code": 90072267492426538, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1431260075643146418, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [196, 14, 1]], [11, [36, 6, 1]]], "qexp_display": "q+(2-2\\zeta_{6})q^{2}-4\\zeta_{6}q^{4}+5\\zeta_{6}q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "e", "char_is_real": false, "Nk2": 12960, "analytic_conductor": 47.7915471046499, "hecke_ring_index": 1, "level_radical": 30, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [810, 3, [731, 487], [1, 3]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [271, 541], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.051", "prec": 17}, {"__RealLiteral__": 0, "data": "1.937", "prec": 17}, {"__RealLiteral__": 0, "data": "0.104", "prec": 17}, {"__RealLiteral__": 0, "data": "11.190", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "97.256", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c3", "trace_display": [2, 0, 5, -14], "traces": [0, 2, 2, 0, -4, 5, 0, -14, -16, 0, 20, -6, 0, -68, 28, 0, -16, 156, 0, 88, 20, 0, 12, -120, 0, -25, -272, 0, 112, -126, 0, 244, 32, 0, 156, -140, 0, -608, 88, 0, -40, 480, 0, -104, 48, 0, -480, -600, 0, 147, 50, 0, -272, -516, 0, -60, 112, 0, 252, -534, 0, -362, 976, 0, 128, 340, 0, 268, -312, 0, -140, -1944, 0, 940, -608, 0, -176, -84, 0, -1244, -160, 0, 1920, -396, 0, 390, 208, 0, 48, -1944, 0, 1904, -480, 0, 1200, 220, 0, 46, 588, 0, 200, 1506, 0, 1474, 544, 0, -516, 1848, 0, 1396, -60, 0, -224, 222, 0, 600, 1008, 0, -2136, -1092, 0, 1295, 724, 0, 976, -250, 0, -3812, 128, 0, -680, -2874, 0, -616, 1072, 0, -1248, 798, 0, 700, 280, 0, -1944, 816, 0, -1260, 940, 0, 1216, -114, 0, -1064, -704, 0, -336, -1220, 0, 1948, 2488, 0, -160, 3360, 0, 4120, 1920, 0, 792, 1248, 0, -2427, 1560, 0, 832, 1146, 0, -350, -96, 0, -1944, -2292, 0, -236, 1904, 0, 960, -1520, 0, -468, 4800, 0, 880, -1692, 0, -3350, -92, 0, 588, -7212, 0, 5392, 200, 0, -3012, -1764, 0, -2400, 5896, 0, 2176, -264, 0, 4, 1032, 0, 1848, -1040, 0, -6832, 1396, 0, 120, -5304, 0, 1162, -896, 0, 888, 2400, 0, 2314, -1200, 0, 1008, -36, 0, -6000, -2136, 0, 2184, 5868, 0, 4330, 5180, 0, 2896, -735, 0, -2992, -1952, 0, -250, 996, 0, 1440, -3812, 0, -256, -642, 0, 4256, -2720, 0, -11496, 7968, 0, -1290, 1232, 0, 1072, -8436, 0, 1696, -1248, 0, -1596, -150, 0, 1504, 2800, 0, 1120, 1308, 0, 5932, 3888, 0, 816, -13440, 0, 2342, -1260, 0, -1880, -5226, 0, 2670, 4864, 0, -456, -8160, 0, -1456, 2128, 0, -704, -3620, 0, 8896, -336, 0, 2440, 9132, 0, 2170, 7792, 0, 9952, -7674, 0, -756, 320, 0, 3360, 6864, 0, 3400, 4120, 0, -3840, -8400, 0, -9596, 3168, 0, 4992, -1340, 0, -12158, 4854, 0, 1560, -2928, 0, -13720, 832, 0, -2292, -10320, 0, 2158, -1400, 0, -384, 330, 0, -4860, 3888, 0, -2292, -17328, 0, -9846, -236, 0, -3808, 2350, 0, -3782, 3840, 0, -6080, 3612, 0, -11276, 936, 0, 4800, 17136, 0, 1960, 880, 0, 3384, 4200, 0, 420, -13400, 0, -368, -13338, 0, -9360, -1176, 0, -7212, -12440, 0, -14384, 5392, 0, -400, 2316, 0, 16592, -12048, 0, -7056, 1824, 0, 12358, 4800, 0, 5896, 14952, 0, -3960, 2176, 0, 528, -3306, 0, 14506, 16, 0, 4128, -1950, 0, -5068, -3696, 0, -1040, -12960, 0, 23788, -6832, 0, -2792, -5280, 0, 12688, 480, 0, -21216, -4968, 0, -4860, -2324, 0, -896, -23016, 0, -5760, 888, 0, -4800, 4760, 0, -1082, 9256, 0, -4800, 11238, 0, 2302, -2016, 0, -36, 31752, 0, -7504, -6000, 0, 4272, -624, 0, -1100, 8736, 0, 23472, -4644, 0, 20672, -8660, 0, 5180, 460, 0, 4852, 2896, 0, 1470, -234, 0, -9828, -11968, 0, -7808, 13608, 0, -14204, 500, 0, 996, 9840, 0, 15060, 1440, 0, 7624, 4458, 0, -6580, -1024, 0, -2568, -7370, 0, -3600, -8512, 0, -2720, 8424, 0, -22424, -11496, 0, -15936, 19032, 0, -2233, -5160, 0, 4928, 32640, 0, 4620, -2144, 0, -8436, -1764, 0, 28036, 1696, 0, 2496, 3490, 0, -18200, -6384, 0, -600, -5544, 0, -17416, -3008, 0, 2800, -23652, 0, 14144, 1120, 0, -2616, 2952, 0, -1110, 23728, 0, 15552, -3084, 0, 4756, -1632, 0, -13440, 6000, 0, -22028, 2342, 0, 2520, -5544, 0, 1548, -7520, 0, -20904, 852, 0, 10736, -5340, 0, 4864, 31092, 0, -10920, -456, 0, 16320, 8616, 0, -17510, -5824, 0, 8512, -6475, 0, 13894, 1408, 0, -3620, 81600, 0, -12992, 8896, 0, 672, 570, 0, 2140, 9760, 0, 36528, 13608, 0, -625, -4340, 0, 7792, -47424, 0, 29320, 9952, 0, 15348, -9530, 0, 9996, -3024, 0, 1280, 456, 0, 23452, -6720, 0, 6864, 14448, 0, 6408, 3400, 0, -8240, -19146, 0, 14370, -15360, 0, -33600, -27810, 0, 30598, 19192, 0, 3168, -6160, 0, 30240, 4992, 0, 2680, -2172, 0, 3778, -48632, 0, 19416, 27198, 0, 644, -3120, 0, -2928, 64632, 0, 7980, -13720, 0, -1664, 17544, 0, -29324, -9168, 0, -41280, -3500, 0, 37440, -4316, 0, -1400, 45564, 0, -26752, -384, 0, -660, 21084, 0, -26054, -19440, 0, 15552, 29280, 0, 2040, 4584, 0, -17328, -11952, 0, -41272, -9846, 0, 472, -3150, 0, 5110, -15232, 0, 9400, -8112, 0, -17336, 7564, 0, 3840, -3216, 0, -27320, -6080, 0, -7224, -1320, 0, 570, -45104, 0, 3744, -12936, 0, -15860, -9600, 0, 17136, -10640, 0, 44320, 1960, 0, -1760, -13116, 0, -9772, 13536, 0, 16800, -36312, 0, -32846, -840, 0, -13400, -23964, 0, -12200, -368, 0, 26676, 21120, 0, 5832, -37440, 0, -4704, -9740, 0, 21076, 14424, 0, -12440, -6216, 0, 49232, -14384, 0, -10784, -22086, 0, -46800, -1600, 0, 9264, -2820, 0, 8400, -33184, 0, -12048, 42768, 0, 10456, -7056, 0, -3648, 10300, 0, -4576, 49432, 0, 19200, 38010, 0, -38642, -11792, 0, 14952, -30864, 0, -7772, -3960, 0, -4352, 11466, 0, -6240, 2112, 0, -13224, -27552, 0, 8513, -29012, 0, 16, -24270, 0, -36260, 4128, 0, 3900, 36480, 0, -15104, -20272, 0, -14784, 12306, 0, 47500, 2080, 0, -12960, 8544, 0, 11460, 23788, 0, 13664, -7464, 0, 18224, -11168, 0, -21120, 1750, 0, 27796, -25376, 0, 480, -79992, 0, -7544, -21216, 0, 9936, 5784, 0, 26684, -19440, 0, -9296, -26400, 0, -5730, 1792, 0, -23016, -61488, 0, -40248, -5760, 0, -1776, -590, 0, 8440, -19200, 0, 19040, 31920, 0, -2376, 2164, 0, 9256, 80472, 0, 69304, -4800, 0, -22476, 66096, 0, 7600, 9208, 0, -8064, -1404, 0, 6468, 72, 0, 31752, -4680, 0, -15308, -7504, 0, 12000, -11298, 0, 57600, 17088, 0, -2496, -28968, 0, -31960, 2200, 0, 8736, 92820, 0, -16920, 23472, 0, 9288, 11172, 0, -29745, 82688, 0, -34640, 16750, 0, 41506, -10360, 0, 460, -36492, 0, -19600, 4852, 0, -5792, -25998, 0, 5832, 5880, 0, -936, -14616, 0, -18030, 19656, 0, -11968, 24960, 0, -5936, -7808, 0, -27216, 13480, 0, 9052, -56816, 0, 2000], "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": 5, "prim_orbit_index": 3, "minimal_twist": "90.4.a.b", "char_is_minimal": false, "conrey_index": 271, "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], [2, -2], [0, 0], [0, -4], [0, 5], [0, 0], [-14, 14], [-8, 0], [0, 0], [10, 0], [-6, 6], [0, 0], [0, -68], [0, 28], [0, 0], [-16, 16], [78, 0], [0, 0], [44, 0], [20, -20], [0, 0], [0, 12], [0, -120], [0, 0], [-25, 25], [-136, 0], [0, 0], [56, 0], [-126, 126], [0, 0], [0, 244], [0, 32], [0, 0], [156, -156], [-70, 0], [0, 0], [-304, 0], [88, -88], [0, 0], [0, -40], [0, 480], [0, 0], [-104, 104], [24, 0], [0, 0], [-240, 0], [-600, 600], [0, 0], [0, 147], [0, 50], [0, 0], [-272, 272], [-258, 0], [0, 0], [-30, 0], [112, -112], [0, 0], [0, 252], [0, -534], [0, 0], [-362, 362], [488, 0], [0, 0], [64, 0], [340, -340], [0, 0], [0, 268], [0, -312], [0, 0], [-140, 140], [-972, 0], [0, 0], [470, 0], [-608, 608], [0, 0], [0, -176], [0, -84], [0, 0], [-1244, 1244], [-80, 0], [0, 0], [960, 0], [-396, 396], [0, 0], [0, 390], [0, 208], [0, 0], [48, -48], [-972, 0], [0, 0], [952, 0], [-480, 480], [0, 0], [0, 1200], [0, 220], [0, 0], [46, -46], [294, 0], [0, 0], [100, 0]]}