# Stored data for newform 1050.4.g.p, downloaded from the LMFDB on 08 January 2026.
{"Nk2": 16800, "analytic_conductor": 61.952005506027646, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 7, "char_orbit_label": "g", "char_order": 2, "char_parity": 1, "char_values": [1050, 2, [701, 127, 451], [2, 1, 2]], "cm_discs": [], "conrey_index": 799, "dim": 2, "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 4, "has_non_self_twist": 1, "hecke_cutters": [[11, [-12, 1]], [13, [3364, 0, 1]]], "hecke_orbit": 16, "hecke_orbit_code": 67554406794527770, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "1050.4.g.p", "level": 1050, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 3, 5, 7], "level_radical": 210, "minimal_twist": "210.4.a.c", "nf_label": "2.0.4.1", "prim_orbit_index": 2, "qexp_display": "q-2 i q^{2}+3 i q^{3}-4 q^{4}+6 q^{6}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "3.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1050.4.g", "trace_display": [0, 0, 0, 0], "trace_hash": 432126660095446784, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.974", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.685", "prec": 20}, {"__RealLiteral__": 0, "data": "0.761", "prec": 17}, {"__RealLiteral__": 0, "data": "137.618", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.508", "prec": 17}, "traces": [0, 2, 0, 0, -8, 0, 12, 0, 0, -18, 0, 24, 0, 0, 28, 0, 32, 0, 0, 8, 0, -42, 0, 0, -48, 0, 232, 0, 0, -588, 0, 256, 0, 0, 168, 0, 72, 0, 0, -348, 0, 564, 0, 0, -96, 0, -96, 0, 0, -98, 0, -252, 0, 0, -108, 0, -112, 0, 0, -936, 0, -500, 0, 0, -128, 0, 144, 0, 0, 144, 0, 1248, 0, 0, -232, 0, -32, 0, 0, -1264, 0, 162, 0, 0, 168, 0, -1712, 0, 0, -1620, 0, -812, 0, 0, 1536, 0, 192, 0, 0, -216, 0, -3780, 0, 0, -928, 0, 552, 0, 0, -1708, 0, 348, 0, 0, 48, 0, 2352, 0, 0, -588, 0, -2374, 0, 0, -1024, 0, -252, 0, 0, 2568, 0, -3144, 0, 0, -2224, 0, -672, 0, 0, -2728, 0, -2304, 0, 0, -288, 0, 3832, 0, 0, -2940, 0, -3776, 0, 0, 336, 0, 1392, 0, 0, -828, 0, 336, 0, 0, -2256, 0, -336, 0, 0, -2334, 0, -72, 0, 0, -3528, 0, 384, 0, 0, -6600, 0, 604, 0, 0, 384, 0, 1536, 0, 0, 378, 0, -8496, 0, 0, -3160, 0, 392, 0, 0, 6512, 0, 3336, 0, 0, 1008, 0, -1184, 0, 0, 96, 0, 11560, 0, 0, -1296, 0, 432, 0, 0, -5748, 0, -4872, 0, 0, 448, 0, -1608, 0, 0, 8708, 0, -504, 0, 0, -2088, 0, 3744, 0, 0, -1488, 0, -3452, 0, 0, 2000, 0, 3384, 0, 0, 504, 0, -12120, 0, 0, 8768, 0, 512, 0, 0, 812, 0, 5292, 0, 0, -576, 0, 112, 0, 0, 12756, 0, -3200, 0, 0, -792, 0, -576, 0, 0, -2304, 0, -1260, 0, 0, -4992, 0, 2784, 0, 0, 6298, 0, 4740, 0, 0, -588, 0, 928, 0, 0, 2784, 0, 5992, 0, 0, 128, 0, -1512, 0, 0, 1776, 0, -432, 0, 0, -424, 0, 5056, 0, 0, -7056, 0, 1944, 0, 0, -648, 0, -4688, 0, 0, -5376, 0, 184, 0, 0, 10656, 0, -672, 0, 0, 2412, 0, 3072, 0, 0, 6848, 0, 7656, 0, 0, 13748, 0, 3132, 0, 0, -5616, 0, 6480, 0, 0, -18528, 0, -13686, 0, 0, 3248, 0, -3000, 0, 0, -5076, 0, -1932, 0, 0, 2016, 0, -6144, 0, 0, 5960, 0, -13152, 0, 0, -768, 0, -9416, 0, 0, -12636, 0, 2016, 0, 0, -12456, 0, 864, 0, 0, -168, 0, -18588, 0, 0, 15120, 0, -8232, 0, 0, 12332, 0, 1188, 0, 0, 864, 0, 3712, 0, 0, 21480, 0, 26908, 0, 0, -2208, 0, 7488, 0, 0, -4176, 0, 20304, 0, 0, 3584, 0, 6832, 0, 0, 14864, 0, 882, 0, 0, -1392, 0, 5824, 0, 0, -4932, 0, 6768, 0, 0, -10416, 0, -192, 0, 0, 2268, 0, -7956, 0, 0, -9408, 0, 8280, 0, 0, 7784, 0, 636, 0, 0, -7584, 0, 2352, 0, 0, -17664, 0, 6728, 0, 0, 9496, 0, 972, 0, 0, 7032, 0, 25560, 0, 0, 928, 0, 4096, 0, 0, 31256, 0, -15984, 0, 0, 1008, 0, -1152, 0, 0, -34380, 0, -13412, 0, 0, -600, 0, -10272, 0, 0, -11484, 0, 34068, 0, 0, 12576, 0, 13152, 0, 0, 23182, 0, 8424, 0, 0, -9720, 0, 8896, 0, 0, -1176, 0, -1076, 0, 0, 2688, 0, -4872, 0, 0, 4500, 0, -2352, 0, 0, 19736, 0, 10912, 0, 0, 49648, 0, -3024, 0, 0, 9216, 0, 21520, 0, 0, 14508, 0, -49352, 0, 0, 7896, 0, 1152, 0, 0, 14124, 0, 1176, 0, 0, -15328, 0, -5880, 0, 0, 1024, 0, 18684, 0, 0, -1296, 0, 11760, 0, 0, -24000, 0, -49484, 0, 0, 15104, 0, -22680, 0, 0, 12348, 0, -44544, 0, 0, -4144, 0, -1344, 0, 0, 42776, 0, -1296, 0, 0, -5568, 0, 6136, 0, 0, 4872, 0, -36608, 0, 0, -26184, 0, 3312, 0, 0, -11232, 0, 11268, 0, 0, -1344, 0, 672, 0, 0, -11232, 0, -5376, 0, 0, -10248, 0, 9024, 0, 0, 39288, 0, 4636, 0, 0, 1344, 0, 2088, 0, 0, -8736, 0, -6000, 0, 0, 34184, 0, 9336, 0, 0, 11060, 0, 15624, 0, 0, 288, 0, -1372, 0, 0, -16008, 0, -1064, 0, 0, 26352, 0, 14112, 0, 0, -12420, 0, 48972, 0, 0, -1536, 0, -30120, 0, 0, -61852, 0, 11376, 0, 0, -3528, 0, 26400, 0, 0, -55008, 0, 4144, 0, 0, -2416, 0, -14244, 0, 0, -1458, 0, 35952, 0, 0, 51776, 0, -1536, 0, 0, 47672, 0, -1392, 0, 0, -6144, 0, -31448, 0, 0, 4536, 0, 44080, 0, 0, -68208, 0, -1512, 0, 0, 1728, 0, 19188, 0, 0, 33984, 0, -39360, 0, 0, -58660, 0, 900, 0, 0, 15408, 0, 12640, 0, 0, 2256, 0, 14976, 0, 0, -1568, 0, -18864, 0, 0, -19728, 0, 5628, 0, 0, -43624, 0, -26048, 0, 0, -32256, 0, 14580, 0, 0, -13344, 0, 29696, 0, 0, -83700, 0, -78008, 0, 0, -2784, 0, -4032, 0, 0, 7308, 0, -26916, 0, 0, 4736, 0, -13104, 0, 0, 41396, 0, -29604, 0, 0, -16368, 0, -384, 0, 0, 30960, 0, 124094, 0, 0, -46240, 0, -13824, 0, 0, -32280, 0, -2784, 0, 0, -7000, 0, 5184, 0, 0, 30200, 0, -11844, 0, 0, -1728, 0, -63272, 0, 0, -15168, 0, 64496, 0, 0, -384, 0, 22992, 0, 0, 8820, 0, -76380, 0, 0, 19488, 0, -23664, 0, 0, -30688, 0, 1944, 0, 0, -17640, 0, -1792, 0, 0, -75264, 0, -11592, 0, 0, 6432, 0, -22656, 0, 0, 34020, 0, -2928, 0, 0, 55976, 0, -34832, 0, 0, 56000, 0, 6216, 0, 0, 2016, 0, -41408, 0, 0, 91740, 0, -392, 0, 0, 5712, 0, 8352, 0, 0, -9204, 0, 71340, 0, 0, -14976, 0, -20544, 0, 0, -111128, 0, 39276, 0, 0, -4968, 0, 5952, 0, 0, 2772, 0, -26814, 0, 0, 13808, 0, 2016, 0, 0, -1008, 0, -78648, 0, 0, -36256, 0, -8000, 0, 0, -19440, 0, 15372, 0, 0, -13536, 0, -49392, 0, 0, -20544, 0, 70768, 0, 0, 17472, 0, -2016, 0, 0, -3132, 0, -9744, 0, 0, 48480, 0, -12384, 0, 0, -64612, 0, -51276, 0, 0, -14004, 0, -35072, 0, 0, -47832, 0, 81868, 0, 0, -2048, 0, -432, 0, 0, 2058, 0, -57120, 0, 0, 18432, 0, -3248, 0, 0, -57088, 0, -39528, 0, 0, -21168, 0, 42064, 0, 0, -63636, 0, -44744, 0, 0, 21504, 0, 2304, 0, 0, 45180, 0, 100380, 0, 0, -448, 0, 65424, 0, 0, -64108, 0, 5292, 0, 0, -39600, 0, -51024, 0, 0, 9744, 0, 18432, 0, 0, 12800, 0, 3624, 0, 0, 21366, 0, -22728, 0, 0, -5680, 0, 3168, 0, 0, 1484, 0, -77664, 0, 0, 2304, 0, -17696, 0, 0, -51804, 0, -45360, 0, 0, -68424, 0, 9216, 0, 0, 47172, 0, -3744, 0, 0, 5040, 0, -13008, 0, 0, 14348, 0, 102312, 0, 0, 2268, 0, 19968, 0, 0, 46704, 0, 16408, 0, 0, -11136, 0, -50976, 0, 0, 59040, 0, 80640, 0, 0, 20648, 0, -25192, 0, 0, -2000, 0, -23112, 0, 0, -18960, 0, 6624, 0, 0, -37296, 0, -63608, 0, 0, -70224, 0, 2352, 0, 0, 28296, 0, -122100, 0, 0, -3712, 0, -93096, 0, 0, -165816, 0, 65436, 0, 0, 39072, 0, -11136, 0, 0, -20496, 0, 13540, 0, 0, -23968, 0, 20016, 0, 0, -44544, 0, -26796, 0, 0, -16384, 0, -512, 0, 0, 6624, 0, 4176, 0, 0, 6048, 0, 113896, 0, 0, 39444, 0, 53824, 0, 0, -20952, 0, -7104, 0, 0, 19656, 0, -80472, 0, 0, 1728, 0, -22680, 0, 0, 139100, 0, 24552, 0, 0, 576, 0, 1696, 0, 0, 10968, 0, 91640, 0, 0, -20224, 0, 69360, 0, 0, 20736, 0, 72192, 0, 0, -11368, 0, 28224, 0, 0, 98816, 0, 10500, 0, 0, -7776, 0, 33904, 0, 0, -171444, 0, 168520, 0, 0, 90912, 0, 2592, 0, 0, 94908, 0, 83868, 0, 0, 18752, 0, 46728, 0, 0, -7056, 0, 576, 0, 0, -34488, 0, 21504, 0, 0, 76944, 0, -90092, 0, 0, -736, 0, -29232, 0, 0, 35496, 0, -60432, 0, 0, 28224, 0, -42624, 0, 0, 34336, 0, 26460, 0, 0, 2688, 0, 116344, 0, 0, 4992, 0, 32956, 0, 0, 62520, 0, -9648, 0, 0, 33984, 0, -166908, 0, 0, -12288, 0, 81168, 0, 0, 94578, 0, -83964, 0, 0, 52248, 0, -27392, 0, 0, 43596, 0, -110756, 0, 0, -30624, 0, -3024, 0, 0, 62112, 0, 37584, 0, 0, 47376, 0, -54992, 0, 0, -149680, 0, -8568, 0, 0, -12528, 0, -928, 0, 0, -23172, 0, 7056, 0, 0, -52920, 0, 22464, 0, 0, 30816, 0, 28812, 0, 0, -25920, 0, -12288, 0, 0, -105628, 0, 7452, 0, 0, -8928, 0, 74112, 0, 0, 61488, 0, -37728, 0, 0, 54744, 0, -20712, 0, 0, -3024, 0, -25224, 0, 0, 116768, 0, -12992, 0, 0, 69224, 0, 54384, 0, 0, 12000, 0, -88472, 0, 0, 46632, 0, 108208, 0, 0, -26688, 0, 20304, 0, 0, 74088, 0, 109620, 0, 0, 7728, 0, 134304, 0, 0, 118364, 0, -26208, 0, 0, 3024, 0, -8064, 0, 0, 116040, 0, -5056, 0, 0, 24576, 0, -72720, 0, 0, 18576, 0, -67920, 0, 0, 11096, 0, -23840, 0, 0, -12544, 0, 21006, 0, 0, 52608, 0, -23912, 0, 0, -32736, 0, 108904, 0, 0, -108576, 0, 3072, 0, 0, 648, 0, -26688, 0, 0, 37664, 0, 132360, 0, 0, 150260, 0, -27648, 0, 0, 4872, 0, 50544, 0, 0, 142320, 0, -20384, 0, 0, -8064, 0, 31752, 0, 0, -63096, 0, -105000, 0, 0, 130256, 0, 49824, 0, 0, 207176, 0, -32256, 0, 0, -3456, 0, -58000, 0, 0, 36456, 0, -49648, 0, 0, 58584, 0, 672, 0, 0, -98136, 0, 89124, 0, 0, 74352, 0, 45984, 0, 0, -172084, 0, 59400, 0, 0, 76536, 0, -60480, 0, 0, -164328, 0, -104804, 0, 0, 32928, 0, -19200, 0, 0, -5436, 0, -28980, 0, 0, -6848, 0, -49328, 0, 0, -35280, 0, 8520, 0, 0, -4752, 0, 162784, 0, 0, 66360, 0, -254272, 0, 0, 88560, 0, -3456, 0, 0, 26544, 0, -45312, 0, 0, -14848, 0, -8232, 0, 0, 62084, 0, 102636, 0, 0, -13824, 0, -85920, 0, 0, 45984, 0, 21206, 0, 0, -107632, 0, -7560, 0, 0, 19512, 0, -6480, 0, 0, -33236, 0, 8832, 0, 0, -114904, 0, -3402, 0, 0, -29952, 0, -189944, 0, 0, 258132, 0, 275184, 0, 0, -61752, 0, 16704, 0, 0, 76464, 0, -57420, 0, 0, -81216, 0, 28224, 0, 0, -3248, 0, -30972, 0, 0, 37788, 0, -14336, 0, 0, 44544, 0, 52780, 0, 0, -27328, 0, 28440, 0, 0, -9936, 0, 24864, 0, 0, 94904, 0, -59456, 0, 0, 101552, 0, 105336, 0, 0, -3528, 0, 186928, 0, 0, 147000, 0, 4032, 0, 0, 55200, 0, 5568, 0, 0, 139644, 0, 22968, 0, 0, -23296, 0, 6144, 0, 0, -211180, 0, -58608, 0, 0, 16704, 0, 19728, 0, 0, 2100, 0, -175820, 0, 0, -27072, 0, 35952, 0, 0, -30024, 0, -147144, 0, 0, -22672, 0, 41664, 0, 0, 27216, 0, 24576, 0, 0, 768, 0, -4032, 0, 0, -119808, 0, -96992, 0, 0, -44016, 0, -9072, 0, 0, -170844, 0, -46032, 0, 0, 31824, 0, 144768, 0, 0, -207354, 0, 31428, 0, 0, 10656, 0, 37632, 0, 0, -28008, 0, -126788, 0, 0, -33120, 0, -2592, 0, 0, 34020, 0, 43440, 0, 0, 28232, 0, -31136, 0, 0, -101968, 0, -864, 0, 0, -2544, 0, -27072, 0, 0, -171300, 0, -64000, 0, 0, -63984, 0, 30336, 0, 0, -104040, 0, 86700, 0, 0, -9408, 0, 124440, 0, 0, -4032, 0, 17052, 0, 0, -42336, 0, 70656, 0, 0, -15120, 0, 33768, 0, 0, -26912, 0, 11664, 0, 0, -50856, 0, -83544, 0, 0, 23072, 0, -37984, 0, 0, -69076, 0, -136368, 0, 0, -3888, 0, -38192, 0, 0, -237132, 0, 71872, 0, 0, -33336, 0, -28128, 0, 0, -70092, 0, 16008, 0, 0, -102240, 0, 69408, 0, 0, -79200, 0, 51732, 0, 0, -32256, 0, -3712, 0, 0, 93432, 0, -75320, 0, 0, -16384, 0, 1104, 0, 0, 43848, 0, 7248, 0, 0, -194824, 0, -125024, 0, 0, 200912, 0], "weight": 4, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [0, -2], [0, 3], [-4, 0], [0, 0], [6, 0], [0, 7], [0, 8], [-9, 0], [0, 0], [12, 0], [0, -12], [0, 58], [14, 0], [0, 0], [16, 0], [0, 42], [0, 18], [4, 0], [0, 0], [-21, 0], [0, -24], [0, -24], [-24, 0], [0, 0], [116, 0], [0, -27], [0, -28], [-294, 0], [0, 0], [128, 0], [0, -32], [0, 36], [84, 0], [0, 0], [36, 0], [0, -58], [0, -8], [-174, 0], [0, 0], [282, 0], [0, 42], [0, -428], [-48, 0], [0, 0], [-48, 0], [0, 384], [0, 48], [-49, 0], [0, 0], [-126, 0], [0, -232], [0, 138], [-54, 0], [0, 0], [-56, 0], [0, 12], [0, 588], [-468, 0], [0, 0], [-250, 0], [0, -256], [0, -63], [-64, 0], [0, 0], [72, 0], [0, -556], [0, -168], [72, 0], [0, 0], [624, 0], [0, -72], [0, 958], [-116, 0], [0, 0], [-16, 0], [0, 84], [0, 348], [-632, 0], [0, 0], [81, 0], [0, -564], [0, -84], [84, 0], [0, 0], [-856, 0], [0, -882], [0, 96], [-810, 0], [0, 0], [-406, 0], [0, 96], [0, 384], [768, 0], [0, 0], [96, 0], [0, -790], [0, 98], [-108, 0], [0, 0]]}