# Stored data for newform 245.4.a.h, downloaded from the LMFDB on 24 April 2024.
{"label": "245.4.a.h", "space_label": "245.4.a", "level": 245, "weight": 4, "hecke_orbit": 8, "hecke_orbit_code": 31525197458702581, "dim": 2, "is_polredabs": true, "nf_label": "2.2.8.1", "trace_hash": 251007577103874342, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [7, 6, 1]], [3, [-17, -2, 1]]], "qexp_display": "q+(-3+\\beta )q^{2}+(1+3\\beta )q^{3}+(3-6\\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": 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": 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": [245, 1, [197, 101], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [5, 7], "conrey_indexes": [1], "field_disc": 8, "field_disc_factorization": [[2, 3]], "field_poly": [-2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.944", "prec": 17}, {"__RealLiteral__": 0, "data": "0.146", "prec": 17}, {"__RealLiteral__": 0, "data": "9.334", "prec": 17}, {"__RealLiteral__": 0, "data": "3.012", "prec": 17}, {"__RealLiteral__": 0, "data": "60.777", "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": [-6, 2, -10, 0], "traces": [0, 2, -6, 2, 6, -10, 6, 0, 6, -16, 30, 28, -66, 36, 0, -10, -14, 76, 72, -160, -30, 0, -44, -22, 162, 50, -148, 2, 0, -250, -30, 132, 42, 148, -444, 0, -192, -416, 376, -84, -30, 106, 0, -666, -156, 80, -402, 196, 130, 0, -150, -572, 348, -952, -402, -140, 0, -472, 510, -840, 330, -98, 4, 0, -602, -180, -236, -1286, 1524, -1426, 0, 1064, 264, 172, 1792, 50, 144, 0, 428, -1240, 70, -754, -438, 1906, 0, -380, 2018, -970, 604, -650, -360, 0, 2742, 1332, -332, 800, -1722, 628, 0, 16, 150, -1418, 1956, 2502, -412, 0, 3424, 1234, 2382, 1070, 220, 1216, 0, 664, 352, 110, 690, -528, 3584, 0, -810, -1870, -1986, -254, -2004, -250, 0, -388, 2934, -606, 740, 592, -804, 0, 4134, -10, -2580, -1736, 3678, -900, 0, 964, -1792, 104, 400, 1250, -44, 0, -4512, 1950, 150, -4412, -1832, -1904, 0, -660, -1308, -2204, 2864, 752, -210, 0, 1230, -1972, 1038, -740, -5698, -1982, 0, -3346, 2220, 656, -2118, 6672, 1170, 0, 284, 2352, 3246, -2540, 960, -2594, 0, -6938, -6150, 2080, -2804, -1096, -948, 0, -1880, -2492, 3790, 1628, 116, 420, 0, 652, -32, 1400, 150, -458, 3534, 0, -3156, -530, -5958, -2632, -732, -3280, 0, 584, -6264, 5264, -4658, 3330, -5142, 0, -2514, 1588, 780, 3528, -5600, -2164, 0, -400, -4592, -764, 4968, -420, 2010, 0, -3870, 4628, 2336, -980, -8904, -3808, 0, 1380, -650, 2612, 6730, -3904, 13386, 0, 1278, -1840, 5596, 1966, 750, -124, 0, -4988, 6124, 2860, -4878, 136, -2158, 0, -1740, 560, 2064, 6338, 3148, 4760, 0, 3238, -5514, -3630, 2010, -11088, -3124, 0, 6824, 700, -678, 1124, 3300, 1344, 0, 3644, -1460, -1908, -5208, 2360, -152, 0, -3864, 4726, -2550, 6628, -2316, -7744, 0, 4200, 5824, -3932, -866, 4284, -1650, 0, 9396, -3578, -128, 490, 8352, 7038, 0, 7146, -20, 2912, 2036, -5128, 6196, 0, 1416, 8684, -7400, -5900, 3010, -1634, 0, -464, 3930, 900, 3148, 3158, -1242, 0, 1180, -13132, 5598, 6592, 11406, 6430, 0, -2808, 8598, -7136, -7620, 5848, -3056, 0, -1738, 7130, -21808, -13246, 7530, 1890, 0, 3996, -5292, -8608, -11032, -5320, -9726, 0, 7156, -1820, -1320, 1786, 3782, 1490, 0, -860, 17946, -15894, -5462, -1568, -8960, 0, -3156, -5352, 1784, -250, 3916, -2100, 0, -5200, -720, 14492, 1116, -7178, 258, 0, -11796, 5448, -10116, 6100, -2140, 24436, 0, 12112, -916, 6200, -48, 16836, 4584, 0, -350, 518, -6066, -1624, 66, 3770, 0, -384, 1404, 6390, 2190, 3112, -1782, 0, 11376, -9530, 6636, 900, 5184, -16440, 0, 13634, -4352, -32, 4528, 1900, -8008, 0, 9438, 584, -10090, 9428, -4766, 2856, 0, 4850, -966, 13928, -3260, -20160, -3020, 0, -15992, -8482, 15360, 3250, 15212, 16902, 0, -12910, 1800, 284, 17592, -15932, 7876, 0, -15248, 21464, 12956, 21460, -13710, 6196, 0, 9474, -1130, -6660, -14292, -10794, -6096, 0, 1660, -3452, 11312, -9124, 3128, -4000, 0, 11024, -3100, -3660, 8610, -12928, -18316, 0, -12330, -3140, 16848, -3636, -29934, -10276, 0, -27676, -3858, 3460, 6848, -80, 3876, 0, 5558, -28420, -750, 14398, 11332, 14606, 0, 7090, 7972, -7666, -30924, -21870, -9780, 0, -12006, 10136, -10472, -12510, 22038, 5304, 0, 1296, 2060, 35332, -2760, -12948, -21264, 0, -7826, -16584, 1460, 30664, -17120, 13104, 0, 3108, -12318, -6170, -270, -3932, 17234, 0, -11910, -942, 25784, -14594, 33348, -5350, 0, -20718, -14904, -12896, -1100, 26240, -12078, 0, -16756, -6080, -6300, -8476, -5648, -12188, 0, -5608, -12452, -25078, -5700, -3320, -5124, 0, 21392, 2500, -1760, -17912, -648, -21572, 0, -550, 13600, 28596, -30594, -19108, -3450, 0, -14116, -7648, 6652, 2640, 14432, 35588, 0, -20960, -17920, 3772, 9440, 14112, 6292, 0, -24054, 27752, -20836, -6680, 4050, -13404, 0, 11944, 9804, 9350, 1506, 22746, 11928, 0, 9930, 968, -21552, 7348, -25214, 1270, 0, 10272, -4878, 18020, 10020, 46310, -18856, 0, 2700, 1250, 18312, -17248, -4116, -45184, 0, 13244, -14848, -7216, -23788, 1940, 33120, 0, 9340, -112, -14670, 13918, 11350, 6156, 0, 3030, 14720, -12134, -15678, -1120, -3700, 0, 10692, 19668, -2358, -2960, -2182, 1456, 0, -11120, 4020, -14898, 41636, -12696, 5978, 0, -29120, 30830, -38706, 23996, -20670, -24172, 0, 14064, 11024, 50, -1398, 22236, 22792, 0, 12900, 15988, -9304, 638, 8496, 8680, 0, 34668, 4902, -22816, -18390, -11108, 30768, 0, 36414, 4500, -25530, 10508, -6470, 3404, 0, 9754, -19156, 19136, 6212, -4820, 19256, 0, 30912, 26830, 8960, 4784, 14898, -48252, 0, -520, -4836, 4500, 37444, 9020, -2000, 0, 11282, -28828, 16218, -6250, -14570, 16938, 0, 31862, 220, -26388, -3606, -29508, 63806, 0, 68334, -15244, 6936, 780, 22560, 2144, 0, 874, 19492, -9750, 24168, -15128, 5736, 0, -750, -5112, 1700, 32756, 6980, 22060, 0, -28748, 10040, -25964, 9160, 24932, -40844, 0, 30684, 9520, 27762, -25760, -14382, -1580, 0, -30056, 46356, -10228, -24496, 3300, 27884, 0, -13964, -5360, 6540, 28896, -88716, 23510, 0, 11020, -28944, 41206, -4284, 39902, -14320, 0, 256, 21036, -48972, -3760, -48504, 24848, 0, -6376, 1050, 12976, 30606, 7128, 43266, 0, 9432, 15402, -13614, -22230, -6150, -57084, 0, -33528, 448, 9860, 6884, 52760, -40426, 0, -5190, 22028, -18136, 25938, 27630, 3700, 0, 14522, -28776, 55340, 28490, -39028, -25476, 0, -7500, 9910, 18096, -39468, 50440, 24820, 0, -3128, -40542, -916, 17352, 16730, 400, 0, 13480, -34452, -11100, -59072, -30912, -57864, 0, -3280, -8726, -39404, -968, 24880, 10590, 0, -32404, 938, 58254, -33360, 35072, -44522, 0, -25920, -5850, -25908, 12258, 6976, -3200, 0, -4260, -27576, 66496, -34144, -1420, -814, 0, -59836, 43032, -11760, 9978, 65906, -21728, 0, -16230, -20876, -58812, -22336, -34022, 12700, 0, -19668, 23730, -40500, -4800, -66848, -412, 0, -31808, 12970, 17484, -29406, -35796, 7024, 0, -18996, -9464, 26884, -86968, 34690, -71436, 0, -79644, -33160, 30750, -5262, -18748, 5152, 0, -10400, -26482, -10728, 30030, -20650, 14020, 0, 16332, -27448, 63338, 5480, 8192, 5928, 0, 3656, 4740, -58188, -3284, 12874, 18648, 0, 14332, -43206, 38352, -1624, 9400, 15476, 0, -34096, -49040, 12460, -2100, -30980, 12964, 0, -18950, -10870, 56896, -15608, 70716, -8140, 0, -25778, 8950, 39520, -580, -33328, -42528, 0, 29644, -2100, -26674, -36716, 16228, 3860, 0, -4384, 86948, -16298, 5946, -3260, 7500, 0, -13488, 4986, 160, -14972, -56028, -6412, 0, -7000, -62838, 58496, 92084, -54272, -750], "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": "35.4.e.b", "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], [-3, 1], [1, 3], [3, -6], [-5, 0], [3, -8], [0, 0], [3, 13], [-8, 6], [15, -5], [14, 10], [-33, 3], [18, -10], [0, 0], [-5, -15], [-7, 12], [38, -54], [36, -26], [-80, -26], [-15, 30], [0, 0], [-22, -16], [-11, -117], [81, 22], [25, 0], [-74, 48], [1, -99], [0, 0], [-125, -60], [-15, 40], [66, 100], [21, -147], [74, 52], [-222, 200], [0, 0], [-96, 66], [-208, 136], [188, -2], [-42, 44], [-15, -65], [53, -30], [0, 0], [-333, 5], [-78, -54], [40, -30], [-201, 340], [98, 64], [65, -9], [0, 0], [-75, 25], [-286, 60], [174, -138], [-476, 142], [-201, 298], [-70, -50], [0, 0], [-236, -266], [255, 55], [-420, 266], [165, -15], [-49, -570], [2, -234], [0, 0], [-301, 366], [-90, 50], [-118, -82], [-643, 69], [762, -390], [-713, -150], [0, 0], [532, 350], [132, -86], [86, 118], [896, -616], [25, 75], [72, 402], [0, 0], [214, -174], [-620, -214], [35, -60], [-377, -258], [-219, 143], [953, 5], [0, 0], [-190, 270], [1009, -348], [-485, -435], [302, 212], [-325, 324], [-180, 130], [0, 0], [1371, -285], [666, 298], [-166, -94], [400, 130], [-861, -84], [314, 500], [0, 0], [8, 4], [75, -150]]}