# Stored data for newform 105.4.a.e, downloaded from the LMFDB on 29 March 2024. {"label": "105.4.a.e", "space_label": "105.4.a", "level": 105, "weight": 4, "hecke_orbit": 5, "hecke_orbit_code": 18014398576590953, "dim": 2, "is_polredabs": true, "nf_label": "2.2.8.1", "trace_hash": 1429840000360424162, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [-7, 2, 1]]], "qexp_display": "q+(-1+\\beta )q^{2}-3q^{3}+(1-2\\beta )q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1680, "fricke_eigenval": -1, "atkin_lehner_string": "+-+", "analytic_conductor": 6.195200550602764, "hecke_ring_index": 2, "level_radical": 105, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 8, "field_poly_is_real_cyclotomic": true, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [105, 1, [71, 22, 31], [1, 1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 5, 7], "conrey_indexes": [1], "field_disc": 8, "field_disc_factorization": [[2, 3]], "field_poly": [-2, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.897", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.307", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "64.904", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[3, 1], [5, -1], [7, 1]], "trace_display": [-2, -6, 10, -14], "traces": [0, 2, -2, -6, 2, 10, 6, -14, -18, 18, -10, -16, -6, -76, 14, -30, -78, -124, -18, -96, 10, 42, -304, -16, 54, 50, 108, -54, -14, 188, 30, -120, 414, 48, 156, -70, 18, -132, 352, 228, -90, 100, -42, -536, 624, 90, 560, -928, 234, 98, -50, 372, -140, 884, 54, -80, 126, 288, 676, 104, -30, -468, -168, -126, 34, -380, 912, -1688, -188, 48, 70, -136, -162, 508, 1188, -150, -608, 112, -324, -432, -390, 162, -1380, -584, 42, -620, -456, -564, 1744, -1404, -90, 532, -1104, 360, 1600, -480, -1242, -1188, -98, -144, 50, -164, -468, -1328, 524, 210, -1908, 1720, -54, 140, -1520, 396, 546, -260, -1056, -80, -1540, -684, 3160, 868, 270, 3866, 1140, -300, 456, 250, 126, -368, -1394, 1608, 540, -632, -1872, 672, 1080, -270, 956, 3164, -1680, 1808, -70, 2784, 2536, -32, -702, 940, -5660, -294, -2244, 3580, 150, 912, -416, -1116, 2128, -600, 420, -1020, 4144, -2652, 2070, 112, -162, 600, 2660, 240, 1928, 96, -378, -1442, 780, -864, 1448, -1028, -2028, -350, -3216, -312, -388, -3040, 90, 108, -756, 1404, -2576, -660, 504, 352, -2272, 378, 1760, 440, -102, 644, 452, 1140, 98, 7236, -2736, -5576, -450, 5064, 2148, -1316, 564, 500, -5328, -144, 3348, -4352, -210, 744, 2932, 408, -7960, -2680, 486, 840, -2828, -1524, 3120, 4776, -3564, -4464, -2898, 450, 836, 3544, 1824, 60, 2800, -336, -6012, -3668, 972, -4640, -6424, 1296, -1092, 4136, 1170, -6124, 1254, -486, -1812, 490, 4140, 4160, 2520, 1752, -250, -10936, -126, -10752, -14096, 1860, 850, 11700, 1368, 924, -700, 1692, -7944, 2368, -5232, 4420, -2464, 4212, -472, 4492, 270, 10744, 5220, -1596, -9948, -400, 3312, -5540, 10352, -1080, 630, 4996, -4800, -11528, -4936, 1440, 11936, -700, 3726, -2074, 3380, 3564, 10812, 5228, 294, 520, -4092, 432, 6436, 1696, -150, 3752, 14960, 492, 6816, -2340, 1404, -840, -4368, 3984, -840, 3056, -1572, 3468, 20188, -630, -7856, 11460, 5724, -18784, 170, -5160, -3920, 6464, 162, -1900, -7544, -420, 5500, 6496, 4560, -4872, -3272, -1188, 5824, -8440, -1638, -1980, -990, 780, -940, 6720, 3168, -686, 9784, 240, -5756, 2088, 4620, 15372, 350, 2052, 208, -21660, -9480, -680, 2180, -2604, -11360, -12856, -810, -5014, -16204, -11598, 980, 2540, -3420, -8240, 7152, 900, 5940, -6188, -1368, -2804, 19232, -750, 4992, -5416, -378, 14088, -3040, 1104, -5272, 3856, 4182, 560, -3908, -4824, 284, -16644, -1620, 2080, -882, 1896, -4100, -2160, 5616, 8532, -4824, -2016, -1950, -12572, -3240, 3984, -4132, 810, -4732, -20064, -2868, 7252, -6900, -9492, 11984, -728, 5040, -2920, -16084, -5424, 17664, -2232, 210, -2756, -11688, -8352, -2836, -3100, -7608, 3276, 14200, 96, -2280, -5240, 2106, -22980, 1176, -2820, 5516, 9472, 16980, 4344, 8720, 882, -7976, 8136, 6732, -7020, 10096, -10740, -238, 11428, -450, 24800, -1412, -2736, 10088, 2660, 1248, 2884, -2972, 3348, -5520, -4692, -6384, 2320, 3036, 1800, 25812, -27016, -1260, 11816, 8000, 3060, -17256, 24128, -12432, -2400, 1316, 7956, 22712, -4032, -6210, 7128, 1260, -336, -6374, -5940, 486, -9280, 852, -1800, -490, 19504, -7980, -9928, -15424, -720, 1224, 952, -5784, 35896, 250, -288, 12344, -31264, 1134, -820, 8960, 4326, 28560, 9580, -2340, -3556, -16194, 2592, -5332, -6640, -4344, -6016, -8316, 3084, 2620, 10756, 6084, 43656, 16520, 1050, -29472, 6864, 9648, -5710, -9540, 936, 4256, -6360, 1164, 8600, 18232, 9120, -17164, -784, -270, 6476, -2008, -324, -26020, 700, 2268, 7464, 16732, -4212, -7600, 4800, 7728, 3024, 9220, 1980, -22512, 9156, -1512, 18384, 2730, -1056, -20484, 12872, 6816, -1300, 18440, -1134, -10776, -25036, -5280, 34536, -23840, -1320, 9660, -400, 306, 7132, -1894, -1932, -7700, 4088, -1356, 13408, 21188, -3420, -32300, -22728, -294, 1152, 15800, -21708, 17820, 5604, 8208, 4340, -16452, 16728, -22624, -36216, 1350, -10940, 3192, -15192, -30832, 19330, -6444, -17648, -22688, 3948, 5700, 36608, -1692, -16420, -16632, -1500, -12208, -23988, 15984, 48848, 2280, 432, -29424, 9828, -10044, 1250, 22868, 13056, -39356, 10296, 630, -16512, -14672, -2232, -34628, -1840, -8796, -3724, -18208, -1224, -6970, 34004, 23880, 7256, 7728, 8040, -23872, -2464, -1458, -66112, 2700, -2520, 14488, 4916, 8484, -3160, -19260, 4572, -11200, 16464, -9360, -53732, 43464, -14328, -1464, 3360, 10692, 27872, -11744, 13392, 5400, -9696, 8694, -12780, 17276, -1350, 3422, 8044, -2508, 8316, 4780, -10632, 14784, 552, -5472, 15820, 686, -180, 9000, -35640, -8400, -12112, 12540, 1008, -17864, 9040, 18036, -8760, -18988, 11004, -350, -836, -2916, 23232, -39312, 13920, 11260, 1148, 19272, -1668, 12680, -3888, 21596, -8832, 3276, -160, 25760, -12408, 49432, -29488, -3510, 9296, -19562, 18372, 32300, 4700, -3762, 7968, -3668, 1458, -28300, 31248, 5436, -41900, 27248, -1470, -9296, 25664, -12420, 7832, -11220, -12480, 13356, 576, -7560, 17900, 14804, -5256, -38816, -12040, 750, -32304, 44256, 32808, -24408, 4560, 378, 29676, -50696, 32256, -2080, 12388, 42288, -980, 10104, -5580, 10768, 2576, -2550, -23500, 10640, -35100, 7172, -42036, -4104, -3000, 14372, -2772, 24676, -25280, 2100, -46912, -36064, -5076, -3822, -5100, 23832, 56728, 964, -7104, 20720, 1820, 15696, 19128, -9332, -13260, 15224, 12508, 7392, 58880, 10350, -12636, 42460, 98976, 1416, 560, 5040, -13476, -8444, -52220, -810, -11408, 10780, -32232, 32736, 3000, -15660, 9856, 30700, 4788, 13300, -28948, 29844, 10496, 45232, 1200, -22120, -13544, -9936, -64260, 9640, 16620, 2612, -6076, -31056, 480, -30976, 3240, 26552, 5376, -1890, 15550, -28732, -14988, 22632, -7210, 14400, -27062, -46764, 34584, 3900, 36960, 14808, 21284, -7980, -4320, 15720, -10524, -35808, -7584, 7240, 2100, 41944, 40448, -11178, -5140, 53284, 6222, -3192, -70784, -10140, 62928, 12180, -10692, -37632, -1750, -32436, -16372, -39768, -15684, -16080, -29356, -882, 44008, 11176, -1560, 39192, -43472, 12276, 2576, -1940, -1296, -15728, 55296, -19308, -15200, 9758, -5088, -38756, -26832, 450, -56856, -30560, -11256, -540, 540, -44880, -54856, -23720, -1476, -3780, -31080, -20448, -22208, -62340, 7020, 5884, 4424, -4212, -4992, -12880, 2520, 88724, 9968, 13104, -3300, 62896, -11952, 29412, -8940, 2520, -4704, -47956, -9168, 46088, 1760, 4716, -3396, -7560, -10404, -11360, -45588, -60564, -44320, 35112, 1890, 69568, 9208, 23568, -29608, 8800, -34380, -6692, 5260, -17172, 2200, -49560, 56352, -48832, -22148, -510, -47198, -49368, 15480, 3604, 3220, 11760, -6512, -60394, -19392, 2260, 66024, -486, -12656, 80384, 5700, 26316, 24796, 22632, 47072, 490, 1260, -28784, 20176, -16500, 36180, -40632, -19488, 26688, -29440, -13680, -34064, -21672, 14616, -17752, -27880, 9816, -65468, -42296, 3564, -2250], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "105.4.a.e", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [-1, 1], [-3, 0], [1, -2], [5, 0], [3, -3], [-7, 0], [-9, -5], [9, 0], [-5, 5], [-8, -20], [-3, 6], [-38, 2], [7, -7], [-15, 0], [-39, 12], [-62, 2], [-9, 9], [-48, 16], [5, -10], [21, 0], [-152, 12], [-8, 34], [27, 15], [25, 0], [54, -40], [-27, 0], [-7, 14], [94, 54], [15, -15], [-60, -18], [207, -11], [24, 60], [78, -64], [-35, 0], [9, -18], [-66, 66], [176, -64], [114, -6], [-45, -25], [50, -80], [-21, 21], [-268, -62], [312, -4], [45, 0], [280, -42], [-464, 42], [117, -36], [49, 0], [-25, 25], [186, -6], [-70, 78], [442, -64], [27, -27], [-40, -100], [63, 35], [144, -48], [338, 40], [52, 204], [-15, 30], [-234, 42], [-84, -42], [-63, 0], [17, 122], [-190, 10], [456, -36], [-844, -38], [-94, 126], [24, -102], [35, -35], [-68, 150], [-81, -45], [254, -322], [594, -132], [-75, 0], [-304, 112], [56, 140], [-162, 120], [-216, 232], [-195, 60], [81, 0], [-690, 130], [-292, 84], [21, -42], [-310, 10], [-228, -206], [-282, -162], [872, 220], [-702, -112], [-45, 45], [266, -14], [-552, 50], [180, 54], [800, -506], [-240, 80], [-621, 33], [-594, -46], [-49, 49], [-72, -180], [25, -50]]}