# Stored data for newform 98.4.c.f, downloaded from the LMFDB on 25 April 2024.
{"label": "98.4.c.f", "space_label": "98.4.c", "level": 98, "weight": 4, "hecke_orbit": 6, "hecke_orbit_code": 22518135642914914, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1407788240705463193, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [64, -8, 1]]], "qexp_display": "q+2\\zeta_{6}q^{2}+(8-8\\zeta_{6})q^{3}+(-4+4\\zeta_{6})q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "c", "char_is_real": false, "Nk2": 1568, "analytic_conductor": 5.78218718056258, "hecke_ring_index": 1, "level_radical": 14, "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": [98, 3, [3], [2]], "hecke_ring_generator_nbound": 9, "inner_twist_count": 2, "level_primes": [2, 7], "conrey_indexes": [67, 79], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.966", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.453", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "103.186", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c3", "trace_display": [2, 8, -14, 0], "traces": [0, 2, 2, 8, -4, -14, 32, 0, -16, -37, 28, 28, 32, -36, 0, -224, -16, 74, 74, 80, 112, 0, 112, 112, -64, -71, -36, -160, 0, 380, -224, 72, 32, -224, 296, 0, 296, 346, -160, -144, 112, -324, 0, -824, 112, -518, -224, 24, -256, 0, -284, -592, 72, -318, -160, -784, 0, 1280, 380, -200, 448, -198, 288, 0, 128, 252, 448, 716, 296, 1792, 0, 784, 296, 538, -692, 568, -640, 0, -576, -240, -224, 359, -324, 2144, 0, -2072, -824, 1520, -224, 810, -2072, 0, -896, -576, -48, 1120, -256, -2708, 0, -2072, -284, -1358, 1184, -832, 288, 0, -1272, -444, 320, -1870, -784, 5536, 0, 2756, 1280, 1568, -760, 666, -800, 0, 1792, 547, 396, -1296, 288, -1512, 0, 3888, 128, -3296, -504, -848, 1792, 0, 2864, 1120, -592, 2966, 1792, -5600, 0, 384, 784, -504, -592, -2660, 2152, 0, -2768, -510, -1136, -592, -640, -5476, 0, -2016, -576, -2686, 480, 2544, -896, 0, 1436, 1012, 648, -3136, 2144, -1088, 0, -3746, -2072, 2960, 1648, 1858, 6080, 0, -896, 1600, -1620, 300, -2072, 4716, 0, -3168, -896, 4844, 1152, -2072, -192, 0, 4480, -1392, 512, -1778, -2708, 4032, 0, 2428, -2072, 1040, 568, -5728, -5432, 0, 4736, 2268, 1664, 4144, 288, 4480, 0, -7736, -1272, 3136, 888, 5768, 1280, 0, -7480, -4304, 1568, -1332, 5536, -7936, 0, 5254, 2756, -3936, -2560, 4810, 6272, 0, -3040, 2182, -1332, 336, -800, -3840, 0, -6000, 1792, 2042, -1094, -5032, 1584, 0, -5184, -1440, -576, 8576, -1512, 1056, 0, 6272, 3888, -8288, -256, 5634, -13184, 0, -2016, -7030, 1696, -168, 1792, 8904, 0, 12960, 2864, -1310, -2240, -2208, -2368, 0, 11864, 1988, -3584, -5294, -5600, -5328, 0, 6484, 384, -1592, -1568, -8960, -2016, 0, -2368, -563, 5320, -10832, 2152, 10044, 0, 5600, -2768, -2240, 1020, -2016, -4544, 0, -2368, 10864, 1280, -2772, -5476, 19072, 0, -13312, -2016, -968, 1152, 3058, -10744, 0, 1920, 4986, -5088, 5320, -896, -7104, 0, 11840, 1436, 1278, -2024, 14960, 2592, 0, -12544, -8612, -4288, 12802, -1088, -20048, 0, -20412, -3746, 11024, 4144, -2016, 11840, 0, 6592, -12544, -3716, -2004, 6080, -2660, 0, 2880, -896, 978, -3200, -5488, -6480, 0, 1200, 9680, 4144, 459, 4716, 8752, 0, -15064, -3168, -8656, 1792, 5994, 19376, 0, 4608, -5278, 4144, -6048, -192, -6840, 0, 12680, 4480, 15552, 2784, -6232, 2048, 0, -7112, 15244, 5416, 14810, 4032, 16576, 0, -13568, 2428, -3360, 4144, 5154, 4160, 0, 2272, -3282, 11456, -1296, -5432, -10052, 0, 19376, 4736, 5810, -4536, -23728, 6656, 0, 16576, -15008, -576, -22400, 4480, -27120, 0, -1476, -7736, 888, 2544, 5254, 12544, 0, 3552, 4032, -11536, -1272, 1280, 10124, 0, -42560, -7480, -8960, 8608, 5640, 6272, 0, -5328, -13388, -11072, 11340, -7936, -8160, 0, -6460, 5254, -4536, -5512, 4736, -15744, 0, -10240, 10646, -9620, -5920, 6272, -14564, 0, 25376, -3040, -8064, -4364, -2816, -5328, 0, 1344, 21488, 1600, -11536, -3840, -11360, 0, 23532, -6000, -3160, -3584, -6228, 8168, 0, -4376, 18956, 10064, 14176, 1584, 16192, 0, -22536, -5184, 14060, 2880, 14504, -2304, 0, 34304, 4460, 3024, -4352, 1056, 3024, 0, 38024, 6272, -14984, -7776, -11790, -33152, 0, -1024, -6400, -11268, -11648, -13184, 1344, 0, 29728, -2016, 1362, 14060, 6968, 6784, 0, -672, -5328, -3584, -377, 8904, 14800, 0, 5832, 12960, -6216, -5728, -2400, -5240, 0, -8960, -7062, 4416, 18864, -2368, 52360, 0, -16392, 11864, -7326, -3976, 15200, -14336, 0, -21176, -38752, 11200, 7466, -5328, 14832, 0, -33152, 6484, 24968, -768, -19292, -6368, 0, -6272, -14250, 17920, -6372, -2016, -22272, 0, -15904, -2368, -8366, 1126, 14224, 21280, 0, -43328, 8904, -4304, 9324, 10044, -40768, 0, 11520, 5600, 9712, 5536, 9378, -8960, 0, 4080, -8320, 4032, 9000, -4544, -15124, 0, -52984, -2368, 7658, -21728, -2976, 5120, 0, -11088, -432, 10952, -4278, 19072, 36288, 0, 37588, -13312, 18040, 4032, -8960, -3872, 0, 4608, 19459, -6116, 17920, -10744, 51208, 0, -43376, 1920, -30944, -9972, -27216, -20352, 0, 21280, -14504, 1792, 10558, -7104, 52304, 0, 92288, 11840, 25584, -2872, 5600, 5112, 0, -8096, -15198, -29920, -11872, 2592, -39812, 0, -12200, -12544, -2318, 17224, 10656, -17152, 0, 51208, 21280, 2176, -31744, -20048, -11088, 0, -20444, -20412, 5680, 7492, 25434, 44096, 0, 16576, 31488, 4032, 8532, 11840, -83048, 0, 76960, 6592, 5724, 25088, 20672, -14864, 0, -8016, 39200, -12160, -11988, -2660, 34912, 0, -42916, 2880, -27680, 1792, -2688, 3912, 0, -12800, 9850, 10976, -8880, -6480, 16128, 0, 14112, 1200, -24000, -19360, -18840, 16576, 0, 1836, -16336, -9432, -13490, 8752, -75008, 0, -61126, -15064, -30488, 6336, 13338, -34624, 0, 7168, -20048, -11988, -17100, 19376, -23040, 0, -39264, 4608, -7140, 10556, -39664, 16576, 0, -24192, -33912, 384, 4224, -6840, 16576, 0, -62772, 12680, 25088, -8960, -34558, 62208, 0, 11136, 38332, 12464, 3600, 2048, -78260, 0, 90144, -7112, -25982, -30488, 5112, 21664, 0, 59240, -12960, -8064, 10976, 16576, -30400, 0, 75208, -13568, 35424, -4856, 1344, -13440, 0, 16576, 3564, -10308, 35616, 4160, 61212, 0, 3552, 2272, 29970, 6564, -15064, 45824, 0, -5184, 10480, 10864, -16810, -10052, 18736, 0, -35328, 19376, 14168, -9472, -32960, 23240, 0, -18144, -34382, 47456, 4472, 6656, 31808, 0, -3432, 16576, -7910, 30016, 42352, -2304, 0, -89600, 7616, -8960, -5760, -27120, 38720, 0, 23422, -1476, 25936, 15472, 26222, 3552, 0, 10176, 12736, -10508, -38752, 12544, -1396, 0, -82880, 3552, -23406, -8064, 7280, -46144, 0, -5088, -9808, -2560, 26012, 10124, -9008, 0, -13440, -42560, -12888, 14960, 50098, -35840, 0, 34432, 8066, -11280, 40176, 6272, -51684, 0, -11384, -5328, 22400, 26776, -13536, -44288, 0, 45360, -10052, 15872, -1920, -8160, -8400, 0, -32256, -6460, 13680, -10508, 23532, -18144, 0, -22048, -33012, -9472, -17004, -15744, 100492, 0, -29136, -10240, 30016, -21292, 22176, -38480, 0, -23680, 1400, -12544, 76288, -14564, -14112, 0, -49132, 25376, -30784, 6080, -13830, -32256, 0, -17456, 7744, 5632, -29008, -5328, 48332, 0, 48928, 1344, -10838, -42976, -18144, 6400, 0, -46144, 40916, 7680, -9684, -11360, 79776, 0, 113236, 23532, -19488, 12000, -42560, -12640, 0, -14336, 24607, 12456, -16428, 8168, 49784, 0, 35008, -4376, 47360, -37912, 23112, 40256, 0, 56704, -10224, -3168, -23874, 16192, 45360, 0, 138380, -22536, -15312, 10368, -16996, 56240, 0, 11520, -46144, -29008, 16528, -2304, -137792, 0, -29120, 34304, -28606, -8920, -27680, 12096], "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, 7, 3, 1, 3, 0]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "14.4.a.a", "char_is_minimal": false, "conrey_index": 67, "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], [0, 2], [8, -8], [-4, 4], [0, -14], [16, 0], [0, 0], [-8, 0], [0, -37], [28, -28], [28, -28], [0, 32], [-18, 0], [0, 0], [-112, 0], [0, -16], [74, -74], [74, -74], [0, 80], [56, 0], [0, 0], [56, 0], [0, 112], [-64, 64], [-71, 71], [0, -36], [-80, 0], [0, 0], [190, 0], [0, -224], [72, -72], [32, -32], [0, -224], [148, 0], [0, 0], [148, 0], [0, 346], [-160, 160], [-144, 144], [0, 112], [-162, 0], [0, 0], [-412, 0], [0, 112], [-518, 518], [-224, 224], [0, 24], [-128, 0], [0, 0], [-142, 0], [0, -592], [72, -72], [-318, 318], [0, -160], [-392, 0], [0, 0], [640, 0], [0, 380], [-200, 200], [448, -448], [0, -198], [144, 0], [0, 0], [64, 0], [0, 252], [448, -448], [716, -716], [0, 296], [896, 0], [0, 0], [392, 0], [0, 296], [538, -538], [-692, 692], [0, 568], [-320, 0], [0, 0], [-288, 0], [0, -240], [-224, 224], [359, -359], [0, -324], [1072, 0], [0, 0], [-1036, 0], [0, -824], [1520, -1520], [-224, 224], [0, 810], [-1036, 0], [0, 0], [-448, 0], [0, -576], [-48, 48], [1120, -1120], [0, -256], [-1354, 0], [0, 0], [-1036, 0], [0, -284]]}