# Stored data for newform 138.4.a.e, downloaded from the LMFDB on 16 April 2024.
{"label": "138.4.a.e", "space_label": "138.4.a", "level": 138, "weight": 4, "hecke_orbit": 5, "hecke_orbit_code": 18014398576590986, "dim": 2, "is_polredabs": true, "nf_label": "2.2.8.1", "trace_hash": 265249732102103332, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [-112, -8, 1]]], "qexp_display": "q+2q^{2}-3q^{3}+4q^{4}+(4+\\beta )q^{5}-6q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2208, "fricke_eigenval": 1, "atkin_lehner_string": "-+-", "analytic_conductor": 8.142263580792205, "hecke_ring_index": 8, "level_radical": 138, "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": [138, 1, [47, 97], [1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [2, 3, 23], "conrey_indexes": [1], "field_disc": 8, "field_disc_factorization": [[2, 3]], "field_poly": [-2, 0, 1], "hecke_ring_index_factorization": [[2, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.004", "prec": 17}, {"__RealLiteral__": 0, "data": "1.861", "prec": 17}, {"__RealLiteral__": 0, "data": "0.019", "prec": 17}, {"__RealLiteral__": 0, "data": "9.078", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "61.627", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, 1], [23, -1]], "trace_display": [4, -6, 8, 12], "traces": [0, 2, 4, -6, 8, 8, -12, 12, 16, 18, 16, 48, -24, 84, 24, -24, 32, 104, 36, 28, 32, -36, 96, 46, -48, 38, 168, -54, 48, 132, -48, -8, 64, -144, 208, -208, 72, -324, 56, -252, 64, -140, -72, -548, 192, 72, 92, -464, -96, -358, 76, -312, 336, 336, -108, -832, 96, -84, 264, 72, -96, 60, -16, 108, 128, 1360, -288, -444, 416, -138, -416, 672, 144, -252, -648, -114, 112, 1312, -504, -1692, 128, 162, -280, -400, -144, -352, -1096, -396, 384, -336, 144, -520, 184, 24, -928, 880, -192, 220, -716, 432, 152, 156, -624, -1836, 672, 624, 672, 2352, -216, -1468, -1664, 972, 192, 2384, -168, 184, 528, 756, 144, 1392, -192, 2586, 120, 420, -32, 1200, 216, 2392, 256, 1644, 2720, 232, -576, -600, -888, -216, 832, 1008, -276, -2104, -832, 1392, 1344, -2080, 288, 3088, -504, 1074, -1296, -1304, -228, 3232, 224, 936, 2624, -2592, -1008, 3276, -3384, -1008, 256, 276, 324, -1376, -560, 2496, -800, -688, -288, 3230, -704, 252, -2192, -3100, -792, -1820, 768, -216, -672, -7800, 288, -6876, -1040, -180, 368, -6928, 48, 5568, -1856, -324, 1760, -3496, -384, -36, 440, -4080, -1432, 2580, 864, -3964, 304, 1332, 312, -1768, -1248, -3632, -3672, 414, 1344, -2400, 1248, 352, 1344, -2016, 4704, 624, -432, 2512, -2936, 756, -3328, 1296, 1944, 1392, 384, 342, 4768, -11752, -336, -3596, 368, -3936, 1056, 9908, 1512, -3392, 288, 5076, 2784, 5872, -384, -6484, 5172, -486, 240, -4504, 840, 4248, -64, 1200, 2400, -1912, 432, 1104, 4784, 1056, 512, 9300, 3288, 3688, 5440, 1188, 464, -5048, -1152, -9152, -1200, 1008, -1776, 7172, -432, -4504, 1664, 1560, 2016, -7280, -552, 6796, -4208, -72, -1664, 2112, 2784, -4236, 2688, -2640, -4160, 2232, 576, -2114, 6176, -660, -1008, 880, 2148, 16160, -2592, -1296, -2608, 1932, -456, -6104, 6464, -468, 448, 12016, 1872, 15568, 5248, 5508, -5184, -3168, -2016, 8116, 6552, -1872, -6768, -3036, -2016, -7072, 512, -7056, 552, -848, 648, 9788, -2752, 4404, -1120, -1248, 4992, 10416, -1600, -2916, -1376, -8688, -576, -12292, 6460, -7152, -1408, 10048, 504, -3192, -4384, -552, -6200, 5960, -1584, 3380, -3640, -2268, 1536, -3124, -432, -11648, -1344, -4176, -15600, 22552, 576, -11022, -13752, -7758, -2080, -14320, -360, 10468, 736, -1260, -13856, 12512, 96, -6820, 11136, -3600, -3712, 15784, -648, 1388, 3520, -7176, -6992, 2440, -768, -7040, -72, -4932, 880, -3952, -8160, 2392, -2864, -696, 5160, -6512, 1728, 14700, -7928, 1800, 608, 6840, 2664, -10576, 624, 648, -3536, 14752, -2496, -15252, -7264, -3024, -7344, -15440, 828, 20928, 2688, 6312, -4800, -8464, 2496, -7932, 704, -4176, 2688, -4168, -4032, -11416, 9408, 6240, 1248, 11504, -864, 19796, 5024, -9264, -5872, 644, 1512, 27872, -6656, -3222, 2592, 7272, 3888, 3520, 2784, 3912, 768, -9116, 684, 8928, 9536, -9696, -23504, -6688, -672, 1324, -7192, -2808, 736, -19340, -7872, 27552, 2112, 7776, 19816, -20312, 3024, 4248, -6784, -9828, 576, -24416, 10152, 6676, 5568, 3024, 11744, 6880, -768, -36136, -12968, -828, 10344, 21872, -972, 18656, 480, 4128, -9008, -18104, 1680, -816, 8496, -7488, -128, 18368, 2400, -21536, 4800, 2064, -3824, -6480, 864, -9616, 2208, -9690, 9568, 23956, 2112, 11800, 1024, -756, 18600, 4176, 6576, -4992, 7376, 9300, 10880, -896, 2376, 15428, 928, 5460, -10096, 7264, -2304, 1058, -18304, 648, -2400, -18168, 2016, 11456, -3552, 23400, 14344, 3696, -864, -23372, -9008, 20628, 3328, -20208, 3120, 24320, 4032, 540, -14560, 9528, -1104, -10408, 13592, 20784, -8416, -14704, -144, -11752, -3328, -16704, 4224, -21576, 5568, -15296, -8472, 972, 5376, 41000, -5280, 12180, -8320, 10488, 4464, 874, 1152, -13956, -4228, 108, 12352, -24928, -1320, 50048, -2016, 12240, 1760, -3016, 4296, -7792, 32320, -7740, -5184, -9548, -2592, -12352, -5216, 11892, 3864, 16192, -912, -8916, -12208, -3996, 12928, -38808, -936, 3040, 896, 5304, 24032, -25632, 3744, 29372, 31136, 10896, 10496, 2464, 11016, -44620, -10368, -1242, -6336, -6880, -4032, -18894, 16232, 7200, 13104, 48, -3744, -2508, -13536, -1056, -6072, 29536, -4032, -27324, -14144, 6048, 1024, -34616, -14112, 17996, 1104, -1872, -1696, 24400, 1296, -61760, 19576, -7536, -5504, 16364, 8808, 15264, -2240, -2268, -2496, -17720, 9984, -47316, 20832, -3888, -3200, -1376, -5832, 3036, -2752, -4176, -17376, -45664, -1152, -14580, -24584, -1026, 12920, 40712, -14304, -19672, -2816, 35256, 20096, 1288, 1008, 25280, -6384, 10788, -8768, -27872, -1104, 14544, -12400, 11808, 11920, -35040, -3168, 1936, 6760, -29724, -7280, -14104, -4536, -21432, 3072, 10176, -6248, 11176, -864, 23364, -23296, -15228, -2688, -184, -8352, -26752, -31200, -17616, 45104, 4416, 1152, -22536, -22044, 19452, -27504, 22988, -15516, 6684, -4160, 1458, -28640, -36944, -720, -8988, 20936, 13512, 1472, 16992, -2520, -15624, -27712, -12744, 25024, -39976, 192, 43168, -13640, -3600, 22272, 12064, -7200, -21444, -7424, 5736, 31568, -15744, -1296, -124, 2776, -3312, 7040, 24988, -14352, 5528, -13984, -3168, 4880, 66512, -1536, 19972, -14080, -27900, -144, 8472, -9864, -20632, 1760, -11064, -7904, -11176, -16320, 73472, 4784, -3564, -5728, 15664, -1392, -42036, 10320, 15144, -13024, 39136, 3456, 49624, 29400, 27456, -15856, 58256, 3600, -19520, 1216, -3024, 13680, 47200, 5328, -4784, -21152, -21516, 1248, 17788, 1296, -2080, -7072, 13512, 29504, 19584, -4992, 776, -30504, -4680, -14528, 31724, -6048, 76344, -14688, 21840, -30880, 47352, 1656, 26868, 41856, -20388, 5376, -9400, 12624, 19776, -9600, 216, -16928, 10040, 4992, -14466, -15864, -6336, 1408, 98936, -8352, 64668, 5376, 12708, -8336, -7452, -8064, 35804, -22832, 7920, 18816, 38948, 12480, -15160, 2496, -6696, 23008, 25248, -1728, -7792, 39592, 6342, 10048, -41632, -18528, -46296, -11744, 1980, 1288, 26144, 3024, -4756, 55744, -2640, -13312, 17264, -6444, -27696, 5184, -48480, 14544, -1328, 7776, -5616, 7040, 3888, 5568, -11104, 7824, -20448, 1536, -5796, -18232, -26128, 1368, 48960, 17856, 18312, 19072, -23408, -19392, 6340, -47008, 1404, -13376, -5376, -1344, -99712, 2648, -36048, -14384, -12944, -5616, 6420, 1472, -46704, -38680, -29120, -15744, -51212, 55104, -16524, 4224, 46244, 15552, -14228, 39632, 9504, -40624, -49408, 6048, -26460, 8496, -24348, -13568, 35640, -19656, -3220, 1152, 5616, -48832, -47416, 20304, -63832, 13352, 9108, 11136, -3144, 6048, -65696, 23488, 21216, 13760, -15200, -1536, -33950, -72272, 21168, -25936, 7024, -1656, 19384, 20688, 2544, 43744, 14680, -1944, 14000, 37312, -29364, 960, 62464, 8256, -27520, -18016, -13212, -36208, 27824, 3360, 77392, -1632, 3744, 16992, -12604, -14976, 12456, -256, -31248, 36736, -78064, 4800, -27068, -43072, 8748, 9600], "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": "138.4.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], [2, 0], [-3, 0], [4, 0], [4, 1], [-6, 0], [6, -1], [8, 0], [9, 0], [8, 2], [24, -4], [-12, 0], [42, 4], [12, -2], [-12, -3], [16, 0], [52, -3], [18, 0], [14, 3], [16, 4], [-18, 3], [48, -8], [23, 0], [-24, 0], [19, 8], [84, 8], [-27, 0], [24, -4], [66, 10], [-24, -6], [-4, -10], [32, 0], [-72, 12], [104, -6], [-104, 2], [36, 0], [-162, -22], [28, 6], [-126, -12], [32, 8], [-70, -12], [-36, 6], [-274, 11], [96, -16], [36, 9], [46, 0], [-232, -6], [-48, 0], [-179, -12], [38, 16], [-156, 9], [168, 16], [168, -41], [-54, 0], [-416, 8], [48, -8], [-42, -9], [132, 20], [36, 62], [-48, -12], [30, 46], [-8, -20], [54, -9], [64, 0], [680, 58], [-144, 24], [-222, -27], [208, -12], [-69, 0], [-208, 4], [336, -56], [72, 0], [-126, -52], [-324, -44], [-57, -24], [56, 12], [656, -48], [-252, -24], [-846, 1], [64, 16], [81, 0], [-140, -24], [-200, 88], [-72, 12], [-176, 40], [-548, 22], [-198, -30], [192, -32], [-168, 19], [72, 18], [-260, -18], [92, 0], [12, 30], [-464, -12], [440, 26], [-96, 0], [110, 82], [-358, -24], [216, -36], [76, 32]]}