# Stored data for newform 33.4.e.a, downloaded from the LMFDB on 20 April 2024. {"label": "33.4.e.a", "space_label": "33.4.e", "level": 33, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 274945015841, "dim": 4, "is_polredabs": true, "nf_label": "4.0.125.1", "trace_hash": 464659941783499964, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [400, -200, 60, -10, 1]]], "qexp_display": "q+(4-2\\zeta_{10}+4\\zeta_{10}^{2})q^{2}-3\\zeta_{10}^{3}q^{3}+\\cdots", "char_order": 5, "char_parity": 1, "char_degree": 4, "char_conductor": 11, "char_orbit_label": "e", "char_is_real": false, "Nk2": 528, "analytic_conductor": 1.9470630301894403, "hecke_ring_index": 1, "level_radical": 33, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 10, "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": 0, "analytic_rank_proved": true, "char_values": [33, 5, [23, 13], [5, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [3, 11], "conrey_indexes": [4, 16, 25, 31], "field_disc": 125, "field_disc_factorization": [[5, 3]], "field_poly": [1, -1, 1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.978", "prec": 17}, {"__RealLiteral__": 0, "data": "0.096", "prec": 17}, {"__RealLiteral__": 0, "data": "51.015", "prec": 20}, {"__RealLiteral__": 0, "data": "0.389", "prec": 17}, {"__RealLiteral__": 0, "data": "1201.833", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c5", "trace_display": [10, -3, -21, 37], "traces": [0, 4, 10, -3, -12, -21, 30, 37, -40, -9, -220, 41, 144, -77, 250, 102, 16, 192, -90, -52, -252, -264, 40, -148, 120, -426, -110, -27, 84, 414, 360, -198, 0, -27, 1140, 477, -108, 201, -830, -231, 480, -129, -570, -132, -1068, -234, -150, -35, 48, 474, -30, -279, 396, 188, 0, 356, -480, 519, 300, -1320, -756, 1275, 330, 333, 832, 638, 30, 150, 2304, 441, -3660, 117, 360, -982, 2450, 867, -2904, 1583, -1320, -1469, -544, -81, 270, -967, 1332, 27, -750, 792, -2440, -5424, -90, -561, 1764, -594, 2000, -707, 1440, 2391, 5280, 1044, 3288, 1065, 630, 706, 1320, 1431, -2410, 1567, -324, -1584, -4270, -3072, -112, -1481, 1140, 887, -6552, 297, -4180, -3054, -2640, -2081, 5580, 123, 2244, 2369, -1710, -766, 4480, -531, 2090, 1342, 1476, 3974, -2430, 918, 840, 2585, -450, 2331, -11136, -930, 5500, 2332, -576, -906, -3460, -2538, 3732, 459, -4200, 1102, -3320, -1782, 13690, 4092, -2772, 984, 6370, 564, 480, -4119, -810, -6086, 2112, -327, -9320, -455, 3000, 3528, -5490, 1557, -2124, -3588, 4860, -10318, 944, 2310, -12790, 3213, 3672, -4625, -4950, -360, 2360, 5321, -4620, 3063, 8280, 189, 390, -803, 2496, 3566, -2820, 264, 5688, 3102, 2250, 396, -120, -4320, 8430, 9582, 6912, 2516, 6180, -657, -1408, -6318, 16860, 6030, -6324, -3774, -15610, 483, -1080, -4609, 1320, 2244, -10368, -10626, -8010, -4605, -12000, 2601, -10270, 4623, -1872, -8758, 13860, -4101, -15360, -1131, -990, 4215, 11220, -4407, -1830, -5275, 1008, 11748, 5490, 972, 15300, 14244, -1830, 8371, 1760, 4089, 17530, 1428, -9504, -4927, -15720, 2691, 2304, 1892, -2250, -2837, 1056, 3726, 4320, -2706, 480, -12272, 13070, 5223, -17280, -3162, -270, 166, 1488, 3597, 12760, -22424, -5328, 12606, -3390, 1683, 3400, -4552, -4350, 4838, 1404, -2706, 15290, -4892, -4320, 12509, -24720, 7173, 7296, 2671, -9540, -5170, 1760, -1593, 7720, -781, -15336, 4029, -20500, 3195, 832, -11265, -7020, -7590, 15396, -7152, 8030, -14693, -1320, -5251, 19860, -8352, 24492, 4865, 8580, -17874, 21632, 4671, -17390, 7989, -972, 6523, 11410, 9108, 1080, -13530, 13380, 23284, -11604, 1809, -12620, -2190, -336, 10376, 15920, 8097, -22176, -132, 8100, -13639, -360, -7734, -8430, -1288, 14904, -12885, -8010, 2376, -14880, 29424, -990, 27647, 20892, -9162, 210, 726, 4320, -12945, -44000, -10743, -15312, -4722, 13140, 12684, 1168, 369, -26980, 15209, -7128, -42812, -3660, -19188, 8000, 7458, 6750, -17379, 13896, 9492, -20350, -10137, 0, 28968, -5220, 2187, -24768, -1635, 6270, 1476, -12720, 441, 12200, 46046, -972, 10560, -2970, 1722, 6816, 12258, -7290, 2299, 8340, -1701, 76560, 24159, 13680, 1552, 11060, -1815, 5832, -20075, 5310, -20712, -15840, 12078, -13880, 17374, 17172, -8830, 8070, -2790, 3920, 1137, -21240, -17295, -74976, -4059, -3660, 9750, 432, -27278, -3740, -2718, 36432, -2256, 840, -28380, 13080, 6696, -38280, -27230, 7236, 28861, 3810, -4413, -30784, 12154, 25740, -5581, -29232, 8046, 10390, -286, -9960, -3512, -38740, -2511, 10644, -6666, -13080, 46802, 8736, -6369, 18300, -14359, -8316, 36450, 11350, -11898, 36080, 5157, -42120, -17822, 20772, -4743, 61720, 694, -17280, -9053, 15660, 13728, 17328, -44754, 2430, 2121, 17520, -18258, -29580, -17213, -4644, 50112, 46420, -10071, -352, -9069, 12930, -15628, 9948, -1365, -14430, -1808, -6840, 18810, -27000, -13296, -9192, 11801, 11250, -13796, 12800, -1404, 9900, 12626, -4752, 6835, 21040, 11391, -4400, 14972, 14580, 13854, 1764, 34416, -6450, -23034, 4272, -33512, -16710, -11880, 6888, -583, -38370, -53168, -12720, -6531, 18480, -10314, -8424, 5577, 27480, 19125, 37440, 10956, 4290, 28551, 31020, -20790, -41500, -59172, -1800, -54457, -47850, 15963, -52128, -3286, 2970, 9471, -14432, 23904, 280, -30885, -1260, 4374, -75200, 567, -28320, 21480, -12360, 47806, 37884, 28116, -7170, 31162, 7488, -26038, 44200, 14613, -42192, 20749, 53460, 21092, 25440, -3663, 11150, 12561, 17064, 16929, 99770, 4341, -4976, 36982, 8370, 35436, 5508, -6237, -3190, 39142, -360, -8767, 7290, 12285, -90816, 59894, 4440, 15710, -18240, -28674, -23520, -17820, -10044, 4458, -14760, -9042, -32200, -73224, -17220, -28633, -25476, -1971, 9650, -59797, -1584, -1776, -53680, -19704, 71568, -53442, -32940, 8199, 2600, 18090, -18010, -64346, 6768, -12672, -31620, 20538, 4480, -2132, 46890, 15704, 21972, 4194, -33630, -5612, 0, 11055, 32780, 11088, 71508, -6883, 3960, -6563, 2064, -8838, -34700, 116556, 12816, -23606, 83290, -9603, 17240, -19296, -24030, -18618, -21600, 7305, -81180, 34770, 17280, 591, 37560, -11502, -15744, -12740, 5730, 49638, -21960, -1716, 35640, 63140, 18684, -14520, 9590, -26274, -3888, 1661, -35760, -53656, -5016, 10017, -50960, -17799, 3600, -2307, 81150, -3393, 137664, 7066, 8910, 66902, -96512, -4380, 65640, -27935, -47520, -45048, -34580, 18369, 57320, 2486, -57420, -1133, -24864, -20310, 50820, 23009, 3024, -2082, 33900, -29376, -55500, -119196, -66750, -12770, -19800, -729, 76500, -22716, 45900, 29958, 68100, -13698, 42240, 45015, 6120, 24627, -96528, -9702, -27200, 15873, 3960, 28784, -104290, -7128, -62064, 137516, -43350, -4122, 560, 4284, 95700, -54848, 11988, -653, -148280, 21129, 29840, 33135, 47760, -80652, -46596, 8073, -26130, -6050, 6912, 23914, -68670, -9174, 42792, -2671, -810, 2167, -24360, -24291, -25810, 557, 22968, -32972, 1380, -14742, 13536, 20994, 12960, 1200, 17364, 2502, 76570, 28512, 360, -81510, 51150, 30159, -24948, 28170, 39210, -18930, 67200, 8739, -660, 3232, 5400, -26999, -13310, -23346, -36680, 9357, 9720, 53837, 114984, -40722, 155170, 130844, -9216, 9696, -31880, 10791, -12108, 24455, 20130, 56143, -3520, 28128, -221540, -67604, 15876, 66329, 50910, 37818, -27456, -3438, 50220, -44110, 12084, 594, 8730, -41355, -43920, -89407, 46390, -13866, -32100, 25688, -9900, -38728, -10848, 27924, -52110, -34387, 4212, -38083, -92760, -6363, -62440, -23760, 6930, -70824, 5796, 11259, -104310, -19094, -12960, 40757, -67740, -47118, 21912, -40196, 31320, 43395, 36960, -18576, -7350, 3437, -35352, 63729, -41970, -8712, -27776, -46250, 4860, 33286, -38412, -15510, -57040, 87157, 29400, 28942, 318340, -7209, 52080, 41255, -20970, -49952, 85120, -2343, 55540, -3498, 31212, 7194, -9590, 1152, -41080, -95750, 52020, 70735, -52044, 6255, 21560, -40535, 11616, 10517, -25500, 34290, -7416, 351, -21060, -9413, -47680, 12015, -15450, 19954, 56988, -54414, 104960, 6354, -14400, 39021, 24090, 15408, 45648, 24561, -69080, -22377, -15840, 27069, 113160, 24507, -41820, -108116, -29880, 11483, -14960, 24354, 47400, -103038, -52884, -2574, -11150, 14595, 45600, 31264, -21690, -47663, 289080, -36522, 91660, -37235, -84864, 24467, -92950, 14013, -117504, -151259, 16470, 74074, -2360, 74412, -91920, 88506, -2916, 70458, -143970, -5016, 1920, 27559, -144540, -67531, -232272, -20196, -105750, 32570, 3240, -14063, 103140, 8835, 100452, -13596, -59760, 71990, -21120, 20157, 193500, -4059, -34812, -50070, -79060, 8397, -24640], "weight_parity": 1, "has_non_self_twist": 1, "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], [1, 1, 11, 3, 1, 5, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "33.4.e.a", "char_is_minimal": true, "conrey_index": 4, "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], [4, -2, 4, 0], [0, 0, 0, -3], [0, 0, 12, 0], [1, -12, 12, -1], [6, 6, -6, -6], [0, 6, -25, 6], [-16, 16, 0, 8], [0, -9, 0, 0], [-42, 0, 26, -26], [-15, 35, -25, 41], [36, 0, 0, 0], [-22, -11, -22, 0], [88, -88, 0, -14], [0, 33, -36, 33], [16, -16, 16, -16], [78, -21, 21, -78], [0, -36, 18, -36], [-45, 45, 0, 83], [-132, 144, -132, 0], [-57, 0, 18, -18], [-42, -12, -48, 172], [-15, 0, 44, -44], [48, -24, 48, 0], [-143, 143, 0, 3], [0, -88, -66, -88], [-27, 27, -27, 27], [228, -300, 300, -228], [0, 192, -30, 192], [78, -78, 0, 126], [-77, 33, -77, 0], [96, 0, 192, -192], [30, 18, 105, -60], [384, 0, 198, -198], [281, -366, 281, 0], [0, 0, 0, -108], [0, -22, -245, -22], [-346, 104, -104, 346], [-99, 33, -33, 99], [0, 104, -272, 104], [-34, 34, 0, -27], [-264, 222, -264, 0], [-75, 0, -84, 84], [-192, -300, 120, 120], [-9, 0, 99, -99], [-148, 294, -148, 0], [55, -55, 0, -200], [0, 0, -48, 0], [-54, 318, -318, 54], [-578, 852, -852, 578], [0, -171, -63, -171], [264, -264, 0, -396], [143, -241, 143, 0], [-54, 0, -108, 108], [295, -571, 202, -51], [56, 0, 352, -352], [135, 114, 135, 0], [-264, 264, 0, 1092], [0, -451, 418, -451], [36, -432, 432, -36], [717, -438, 438, -717], [0, -22, -374, -22], [54, -54, 0, 171], [0, 832, 0, 0], [209, 0, 99, -99], [-180, 552, -36, 162], [-243, 0, -561, 561], [684, 252, 684, 0], [132, -132, 0, 45], [0, -902, 1856, -902], [-433, 708, -708, 433], [72, 72, -72, -72], [0, -318, 346, -318], [1024, -1024, 0, -622], [429, -420, 429, 0], [-996, 0, -540, 540], [94, 745, -496, -34], [-462, 0, -264, 264], [-702, 637, -702, 0], [-176, 176, 0, -16], [0, 0, 81, 0], [-82, 258, -258, 82], [-35, -431, 431, 35], [0, 216, -900, 216], [-174, 174, 0, 549], [-132, -354, -132, 0], [486, 0, 576, -576], [-496, -192, 24, -240], [-1279, 0, 154, -154], [-234, 612, -234, 0], [-352, 352, 0, 495], [0, 528, -708, 528], [-132, -99, 99, 132], [620, 70, -70, -620], [0, -373, -39, -373], [576, -576, 0, -288], [891, -282, 891, 0], [948, 0, -744, 744], [369, -234, 54, -144], [-36, 0, -1716, 1716]]}