# Stored data for newform 245.4.a.j, downloaded from the LMFDB on 19 April 2024.
{"label": "245.4.a.j", "space_label": "245.4.a", "level": 245, "weight": 4, "hecke_orbit": 10, "hecke_orbit_code": 40532396713443573, "dim": 2, "is_polredabs": true, "nf_label": "2.2.44.1", "trace_hash": 1340805550264410612, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-10, -2, 1]], [3, [-5, 1]]], "qexp_display": "q+(1+\\beta )q^{2}+5q^{3}+(4+2\\beta )q^{4}+5q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 3920, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 14.455467951406451, "hecke_ring_index": 1, "level_radical": 35, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "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": [245, 1, [197, 101], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [5, 7], "conrey_indexes": [1], "field_disc": 44, "field_disc_factorization": [[2, 2], [11, 1]], "field_poly": [-11, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.082", "prec": 17}, {"__RealLiteral__": 0, "data": "1.923", "prec": 17}, {"__RealLiteral__": 0, "data": "0.456", "prec": 17}, {"__RealLiteral__": 0, "data": "8.951", "prec": 17}, {"__RealLiteral__": 0, "data": "3.227", "prec": 17}, {"__RealLiteral__": 0, "data": "56.583", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[5, -1], [7, -1]], "trace_display": [2, 10, 10, 0], "traces": [0, 2, 2, 10, 8, 10, 10, 0, 36, -4, 10, 66, 40, 10, 0, 50, -72, 70, -4, 140, 40, 0, -22, -16, 180, 50, 450, -290, 0, -258, 50, -20, -360, 330, -370, 0, -16, 328, 580, 50, 180, 300, 0, -116, 88, -20, -632, -30, -360, 0, 50, 350, 920, 540, -290, 330, 0, 700, -1314, 380, 200, 1080, -1340, 0, -224, 50, -110, 468, -600, -80, 0, -1056, -72, -860, 1296, 250, 1440, 0, 2250, 158, -360, -1342, -1900, 40, 0, 350, 148, -1290, 1364, -240, -20, 0, -1296, -100, -910, 700, -1800, 1630, 0, -132, 200, -2020, -1850, -30, -700, 0, -2100, -180, -1160, -1902, -110, 1640, 0, 2376, 2900, -80, -3144, -20, 1260, 0, 900, -132, -240, 1500, -2720, 250, 0, -3668, -1744, -580, 2250, -240, 440, 0, -1644, -1450, 2140, -2440, -3160, 5600, 0, -150, 352, -1430, 144, -1290, -5260, 0, 3248, -268, 250, -1026, 1640, -140, 0, -100, 4600, -980, 7814, 2700, -1800, 0, -1342, -5520, -3200, 1650, -4360, 2250, 0, 4456, -1850, -280, 64, 5750, -6570, 0, -2376, 1900, 8120, 232, -80, -3940, 0, 5400, 944, 1640, -6700, 4070, -1880, 0, 2900, 306, -1120, 5024, 5590, 250, 0, 1428, 44, 8660, 900, 2340, 1060, 0, -3000, 1500, 5250, 32, -360, 2860, 0, -9314, -3120, -5280, -3700, -580, -5220, 0, 4434, -4300, 440, -8450, 6480, 2810, 0, -100, 3872, 2250, 7200, -220, -3160, 0, -2532, 4176, -900, -150, 3280, 790, 0, -4002, -1800, 4760, -5940, 1120, 1680, 0, -9500, 9500, 2280, 200, 250, 1080, 0, 1936, -5076, 1750, -3296, 2460, 740, 0, 4600, 516, 8120, 3116, 6820, 2700, 0, -1200, -2352, -3840, -1450, -2120, -2520, 0, 2400, 1650, -6480, -1240, 5600, 40, 0, 1446, -4550, 3750, -1408, 3500, 12650, 0, 720, 1424, -6570, 8150, -12240, -11730, 0, 1900, 3968, -9570, 8356, -12400, 1000, 0, 8742, -10100, -5040, 5400, 740, -570, 0, -150, -6700, -6620, -3500, -4710, -4500, 0, 15944, 12772, -10500, -4290, -1120, -900, 0, -3900, -5368, 250, 2400, -9510, 9800, 0, -550, -1496, -8640, -656, -12710, 2340, 0, -2080, 8856, 11880, -3000, 4620, -1160, 0, -2616, -400, 3550, 6888, -15720, 2980, 0, -1450, -10120, -11690, 6300, -5280, 15760, 0, -8568, -5152, -360, 4882, -10980, -660, 0, -4300, -1200, 22210, 576, -600, 6480, 0, -13600, 4256, -13530, 1250, 1220, -22410, 0, 6208, 7200, -18340, -15094, -8160, -8720, 0, -1752, 232, 14440, -14838, 11250, 11760, 0, -1200, 19116, 790, -176, -9010, 10420, 0, -1800, -11526, -8220, -26500, -1920, -6710, 0, 6952, 10700, -3900, -9500, -12200, 10440, 0, 1264, 200, -10600, 28000, 11220, -2820, 0, -3294, -11514, 60, 15000, 1750, 1760, 0, -7760, -7150, 740, -7366, 10440, -11300, 0, -6450, 5064, -13440, -26300, -5560, 6820, 0, 4750, 6780, 16240, -1200, 18650, -1340, 0, 11582, -100, 18700, 12496, -5130, 20730, 0, 8200, -9292, 2860, -10150, -6480, -31240, 0, 13760, 9288, -500, 33392, 9310, -1840, 0, -4550, -4900, 5080, -4884, 39070, 3500, 0, -1080, 6998, -3080, -9000, 21000, 4320, 0, -12144, 8150, 1120, 13912, 22080, -27600, 0, 16286, -16000, 12090, 42500, -660, 720, 0, -21800, -10422, 1000, 11250, 23960, 2830, 0, -10100, -17688, 22280, -17488, -6640, -9250, 0, 23328, -20300, 9500, -150, 320, 2530, 0, 28750, -3500, 19260, 2628, 16640, 15760, 0, 34972, 25700, -11880, -6958, -10500, -760, 0, -42500, 40600, -900, 12648, 1160, 2320, 0, -5800, -9786, 9760, -19700, -3800, -9510, 0, -12632, -80, -2160, -550, -39180, 4720, 0, -20600, 8200, 22400, -14328, 2680, 4700, 0, 20350, -34282, 37160, -9400, 11880, -22650, 0, -21824, -33628, 14500, 20056, 22440, 1530, 0, -400, 448, -32030, -29376, 25120, -15720, 0, 27950, 28380, -6680, -100, -16570, 20680, 0, -27800, 6300, 7140, -11808, -1110, 3190, 0, 16176, 43300, -19000, -8718, 4500, -26420, 0, -936, 15432, -660, 5300, 13750, -34000, 0, -1200, -17750, 1200, -35044, -16410, 7500, 0, -792, 26250, 3080, -13600, 2320, 9660, 0, -1800, 1250, -11310, 14300, -10960, -7880, 0, -646, -12468, -46570, 21044, -18340, -15600, 0, -27786, 2112, -8720, 27564, -18500, 10170, 0, -2900, -19300, 12520, -24156, 9020, 11250, 0, -6240, -37500, 22170, -1200, -10800, 1720, 0, -1158, 2200, -2600, -18568, -42250, 9520, 0, -2592, 31632, -20920, 14050, -8220, 40920, 0, 10080, -10000, -7250, 26624, -26350, 19360, 0, 10700, 11250, -38060, 14584, -2880, -12200, 0, -1100, 4176, -50100, -15800, -23320, 18600, 0, 816, 28000, -12660, 54500, 1660, 20880, 0, -22946, -65250, 42320, 10208, -750, -24450, 0, 16400, -35858, 1760, -316, -21040, 37120, 0, -7150, -16672, -20010, -3216, -7840, 720, 0, 66482, 23800, -29840, -6450, -29700, -1120, 0, 41834, -26300, -9340, 8400, 30370, 19570, 0, 15200, 23892, 3800, -12262, 16240, 47500, 0, 3060, 11400, -1340, -15368, -80, -18920, 0, 1250, 2654, 1080, 5400, -84450, -5130, 0, -15728, 20464, 9680, 8200, 52960, -25380, 0, -29576, -700, -55680, 19500, -16480, -28420, 0, 12300, 6544, 6730, -296, -500, 21420, 0, -22054, -23000, 23000, -40480, -6280, 37410, 0, -4900, 40600, 41090, 41088, 15580, 39070, 0, -2728, -21000, 41590, 13500, 38160, 20070, 0, 16550, -9000, 480, -47958, -10780, -11760, 0, -37500, -19200, -42520, -5398, -6710, 20880, 0, -10600, 24464, -27600, -12600, -2840, -43500, 0, -16000, 31474, 12000, -3364, -11100, 8250, 0, -5712, 2592, -59380, -21800, -6200, -89120, 0, 28000, 11250, 28160, 2900, -28340, 6360, 0, 35192, 17298, 7230, -41656, 22280, 1820, 0, -19440, 18750, -9250, -29728, -7040, -32380, 0, -1400, 3800, -29900, 63250, 57160, 320, 0, -84366, -12396, 52200, 28750, 27420, 7120, 0, -25410, -32850, -39900, -46908, -3260, -60080, 0, -61200, 13500, 36680, -58650, -11880, -17920, 0, 43304, -7400, 9500, 16900, 6240, 19840, 0, 40600, -44286, 42920, -19700, 41780, 1160, 0, -62000, 20206, 65940, -400, 71700, -67100, 0, 39776, -19700, 43710, 19240, 45960, 4040, 0, -18816, -25200, 18920, 55036, 27000, 5280, 0, 53650, -28978, 4720, -2850, -38280, 22880, 0, 8200, 71400, 60, 67560, -6900, -33500, 0, 75136, -33100, 510, 20350, 1400, 17270, 0, -23550, -9400, 48760, -22500, 59200, -13680, 0, 8932, 20820, 79720, -92300, 14500, 63860, 0, 50924, 4200, 1530, 5992, -21450, -89760, 0, -5600, 19818, 98000, 360, 18160, 25120, 0, -56860, 9240, -19500, 27950, -25220, 4480, 0, -44696, 1250, -38880, 17292, 12000, -41360, 0, 3804, -16362, -30650, 49000, 7140, 31890, 0, 104000, -6464, 220, -936, 30000, -7480, 0, 43300, -43200, -21210, 88578, -47560, 4500], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "245.4.a.i", "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], [5, 0], [4, 2], [5, 0], [5, 5], [0, 0], [18, -2], [-2, 0], [5, 5], [33, -4], [20, 10], [5, 20], [0, 0], [25, 0], [-36, 0], [35, -20], [-2, -2], [70, 20], [20, 10], [0, 0], [-11, 29], [-8, -28], [90, -10], [25, 0], [225, 25], [-145, 0], [0, 0], [-129, -48], [25, 25], [-10, -60], [-180, -20], [165, -20], [-185, 15], [0, 0], [-8, -4], [164, 44], [290, 90], [25, 100], [90, -10], [150, -100], [0, 0], [-58, 12], [44, 50], [-10, 0], [-316, -36], [-15, -40], [-180, 0], [0, 0], [25, 25], [175, -100], [460, 90], [270, -120], [-145, -145], [165, -20], [0, 0], [350, 100], [-657, -177], [190, 40], [100, 50], [540, -60], [-670, -70], [0, 0], [-112, -200], [25, 100], [-55, 145], [234, -96], [-300, -10], [-40, -140], [0, 0], [-528, 64], [-36, 4], [-430, -200], [648, 208], [125, 0], [720, 220], [0, 0], [1125, 125], [79, 348], [-180, 0], [-671, 0], [-950, 50], [20, -200], [0, 0], [175, -100], [74, -46], [-645, -240], [682, -138], [-120, 380], [-10, -10], [0, 0], [-648, -128], [-50, -300], [-455, -55], [350, 100], [-900, -100], [815, 180], [0, 0], [-66, 8], [100, 50]]}