# Stored data for newform 198.6.e.b, downloaded from the LMFDB on 01 June 2024. {"Nk2": 7128, "analytic_conductor": 31.755996322970166, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 9, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 3, "char_parity": 1, "char_values": [198, 3, [155, 145], [1, 3]], "cm_discs": [], "conrey_index": 67, "dim": 24, "has_non_self_twist": 1, "hecke_orbit": 2, "hecke_orbit_code": 4503874605940934, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 9, 3, 1, 3, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "198.6.e.b", "level": 198, "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, 11], "level_radical": 66, "minimal_twist": "198.6.e.b", "prim_orbit_index": 3, "related_objects": [], "relative_dim": 12, "rm_discs": [], "sato_tate_group": "5.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "198.6.e", "trace_display": [48, 21, -7, 24], "traces": [24, 48, 21, -192, -7, 168, 24, -1536, -543, -56, -1452, 336, -688, -96, -1500, -3072, 3512, 1164, -3836, -112, 1842, 5808, -680, -1344, -7759, -5504, 3024, -768, -3210, -4596, 857, 12288, -5082, 7024, 29824, 13344, 7166, -7672, -23076, 448, -27726, -10680, -15092, 46464, 38667, -5440, -28938, -10752, 17322, 31036, 37032, -11008, -12652, 59832, 1694, -1536, -168660, 12840, -33123, 5616, 36262, 6856, 47496, 98304, -31470, -10164, 35563, -28096, 123459, 59648, 295146, 34752, 12056, 14332, -244221, 30688, 2904, -64200, 128058, 3584, 90621, -221808, -209888, -72192, 228182, 60368, -89802, 92928, -46724, 96972, -305924, -10880, -187767, 115752, -118660, -21504, 240799, 138576, -35211, 248288, -160108, 1656, 258740, 44032, -506004, -25304, 231928, 190944, -155356, 3388, 209748, 6144, -485275, -279240, 220129, 102720, -314904, -264984, -218726, 96000, -175692, -145048, -530370, 13712, 1228602, -131376, 216452, 196608, 128940, 125880, -574748, 40656, 94904, 284504, -379503, -224768, -734449, 658428, 396960, -238592, -264006, 590292, 166496, -74496, -443340, 24112, 73251, -57328, -1144090, 468012, 390892, 245504, -38850, 23232, -253362, 112416, 1707, -512232, -728013, 7168, 925460, -75096, -2274272, -443616, 139029, 839552, -1599672, -117888, 920266, 1825456, -1884024, 482944, -387934, -398520, 988504, -371712, 156735, -93448, 1027058, -230784, 1800286, -611848, 2142420, 43520, -1004754, 172248, -212476, 926016, -1912356, -949280, -1108737, 86016, 688894, -963196, -1908774, 277152, 2478532, -403656, -2401872, 496576, 2170938, 640432, -1307472, -585888, 167268, 2069920, 1128516, 352256, 232078, -236160, 563112, 101216, 38646, 463856, 1377128, -193536, -363848, -310712, 2632602, -13552, -138126, 1166628, 1846142, 49152, -2459871, -3882200, -670302, 1581600, 3135162, -880516, 323070, 205440, -1727348, -4799184, -4421286, -529968, 4655310, 874904, 13838, 294144, 689872, -1405536, -2292219, -1160384, -471249, 2023200, 3446944, -54848, -428256, 2457204, 6529376, -1285440, 164560, 432904, 4973862, -786432, 183716, 1354344, 5041864, 1007040, -7529688, -4597984, -1256988, 325248, 5690909, -379616, -2490261, 569008, 2468180, -7481592, -7769508, -449536, 3056352, 2937796, -938839, 658368, 737430, 3175680, -4281105, -1908736, -358468, 3819060, 3447784, -2361168, -2459454, 332992, -734040, -854016, -2980204, -886680, 10942017, -96448, 87088, -543780, 3461130, -458624, -1809918, -9152720, -3680970, 5779584, 6993056, -1563568, -3715020, 491008, 8069384, -5437992, -6141188, 46464, 9702027, 1013448, -8134790, 1476864, 4126128, 13656, -8921928, -4097856, -10455018, 5734944, -388410, -28672, 351660, 1850920, 3479312, -1750320, -4030744, -4548544, 13437948, 1774464, -4305834, -169884, 8608149, 6716416, -10374780, -12797376, -5184307, 683520, 3664028, -3681064, -4600689, 3650912, -207394, -6527664, 6886656, 965888, 21610701, 1551736, 3472838, -157248, -454786, 7908032, -15128442, -2973696, 276648, 4178952, 1374756, 373792, 6240870, 2054116, 15129516, -2474688, -12857724, 3600572, 307461, 2447392, -10315500, 10312152, 3974781, 348160, -28889460, -8038032, -10456568, 3693264, -3021266, 849904, 5040279, 1852032, 21175824, -17290368, 559320, -1898560, 12198000, 4434948, -11153491, 688128, -1804352, 5511152, -25419852, -7705568, 333903, -981648, -2163986, -1108608, 24942318, 4957064, 13235440, -1051248, 2875348, -4803744, 18071868, -1986304, 7143052, 11701260, -6638996, 5123456, -11223396, -10459776, -433543, -2370048, -9970196, -669072, 19283751, 4139840, 4791252, -8497212, 14062024, 704512, -2349588, -928312, -14091642, 7151424, 1202448, 4504896, -20044125, 809728, -22026476, -5575644, -12440866, -1855424, 1942050, 2754256, 32703516, -3829248, 13270800, -727696, 19738656, 1242848, -15851030, 18072264, -2677574, -108416, -26245980, -1105008, -20615813, 1310544, -4727309, -7384568, 6256650, 98304, 11322434, -16542540, 6709692, -7764400, -2791974, 2681208, 421866, 10794240, -15601682, 25081296, -14319396, -7044128, -28252822, 2183808, -11689756, -821760, 22943772, -3454696, 41397666, -14158272, -6510292, -8842572, -12446580, 2119872, -1826132, 21097704, -16795050, 6999232, -34047411, 110704, -19757382, -359424, -4622102, -2759488, 31705764, -2811072, 46352096, -16274844, 29278290, -2320768, -24489909, 1884996, -41205910, 16578720, -11876766, 27575552, -2933403, -438784, -22887912, 6200472, -10626384, -9828816, 26617338, 13058752, 45315056, -3039744, 23099864, 329120, -5615694, -1731616, -3944890, 28637040, -7221068, -6291456, -13439790, 1469728, -32098263, 3354336, -3501498, -20167456, 21995532, 2014080, 50897334, -30433392, -9933540, -9195968, -18932406, 5027952, -45747762, 650496, -13657318, 45527272, -18323631, -3036928, -32840340, -3559176, -11331698, -2276032, 34448109, 4936360, -4191924, -23854320, 55637512, -15539016, 51280011, 1798144, -34135398, 43563048, -21593910, 23502368, 19641024, -7510712, -24242238, -7901376, -1074288, -2949720, 35785242, 6351360, 43656696, -21899976, -28555316, -3817472, -50094, 1433872, -16015970, 19500336, -18901294, 27582272, -35173044, -18889344, -16414952, -27824136, -17923580, -1331968, 39472155, -1468080, 116584166, -2224128, 24848526, -5960408, -44877822, 3546720, -42077500, 47608764, 765446, -771584, 2052144, 696704, -16878864, -3347136, -1332530, -13844520, 52203342, -917248, 60526032, -5776056, 50397220, -18305440, -11020539, 14723880, -31883580, 15630144, -4427078, 55944448, -16175673, -12508544, -102487, -22819296, 479974, -1964032, 2358378, 16138768, 16750476, -21130368, 68115824, -12282376, -75267216, -185856, -13972000, 93275484, -9570927, 8107584, 38178936, -65078320, -41427988, 4108800, -39456166, -16504512, 8447010, 27312, 44282568, -45877056, 34392862, -8195712, -18609438, 41820072, -28446768, 34587984, -22366200, -3107280, 2727360, -229376, -31590606, -6817608, -13652784, -7403680, 37877856, 6958624, 84891284, -5799744, 8015766, -8061488, -105061944, 18194176, -29992905, 77520288, -24300710, 14195712, -15343194, -34446672, -4160070, -2904000, -46317871, -34432596, 42475302, 13432832, 26011828, -80535300, 81216204, -25594752, -22750158, 20737228, 4387702, 4620288, -40921374, 29312224, -41958279, -29448512, -17810768, -55765536, -85965376, -14603648, 51456888, -414788, 15412332, 4033728, 40540892, 13773312, -17464701, -3863552, -14568774, 117293376, -26115211, 12413888, 3974124, 27782704, -40789352, 5747328, -8100234, 1819144, -29376006, 15816064, 99363192, -69646176, 90673264, -5947392, -67381173, -1106592, -38752358, 14208048, -58632373, 10998048, -37984056, 2990336, -33845061, -51019440, -3807870, -8216464, 53320368, 30259032, 753054, -6206208, 133497148, -25715448, -30288612, -14402288, -35814894, -1229844, -57718945, 19579136, 3547206, -82524000, 6624152, 6969888, -78052950, -15899124, -21277071, 696320, -8606246, -129734352, 68170308, -16076064, 87187590, 41826272, -28939040, 12017088, -52626022, -24170128, -8292846, 6799232, 6221624, -77354172, -7454217, -7408128, 7669527, 42351648, 72480740, -38563776, 34024896, 1118640, -19917447, 7594240, -89672436, 93899712, -21534662, 35479584, -80638602, -89227928, 4166544, 1376256, 14248096, 7217408, 74068860, 11022304, 43031400, -76447584, 201451190, -15411136, 46006086, -1335612, -5373450, 26613792, -17856333, -17311888, 62249796, -8868864, 44791993, 27601224, -92839766, -19828256, 64479060, 26470880, 73536400, 2253504, 188488444, 5750696, 49266732, 19214976, 23831961, 88225320, 5162160, -15890432, -50259441, 57144416, -729388, 12070032, -46028428, 26555984, -64899867, 10246912, -65283536, -112697964, 94583676, -20919552, 53532996, 1734172, 31008233, -105984, -24466644, -79761568, -22357860, -5352576, 2887912, -37016508, -15009780, -16559360, -14157363, 9582504, 66917324, -52045104, 132453862, 28124048, 39884856, -2818048, 25987578, 84863136, -94584462, -7426496, -74576529, -112733136, 34172412, 32384256, -96927336, -4809792, -68997906, 9009792, -911210, -69998904, -702768, 1619456, -71314764, 88105904, 70559295, -22920912, -58282474, -99526928, 26748714, -14843392, -71802034, -3400584, -62487623, -11017024, -36671184, 65407032, -57942376, -12220416, 25242164, 26541600, 120883257, 2910784, 15495018, 160755048, -2869082, 9942784, -15794793, -126808240, 68210052, 30167424, -17629648, 10710296, -83986734, -216832, 7799458, -68318388, 118245988, -2210016, 109280646, 82463252, -43655784, -13423872, -35581298, -37818472, 2271654, -59076544, 38404176, -89002032, -21381043, -393216, -101848050, 22644868, -50853612, -26812224, 55355204, 13419384, 41666316, 31057600, 2174309, 86831592, 27861028, 21449664, 82728318, 3374928, 1335162, 17871360, -25396448, 62406728, -159153690, 50162592, -57761008, -97716960, -134502156, -14088256, 37880892, 113011288, 16159512, 3566112, -53717851, -93518048, 59129628, -6574080, 30320394, 24547032, 105210522, 13818784, -188998473, 82795332, -55220044, 20153856, 21299752, -13020584, 124012734, 35370288, 15850044, 63334740, -136730178, 16958976, 42662214, -14609056, 58313445, 9905856, 29077324, 67180200, -152250084, 13998464, -67106448, -81465420, -220928130, 221408, 12055230, 79029528, 51935956, -6144000, 74134357, -36976816, -7037346, -22075904, -66066208, -14694048, -58609064, 11244288, -67779894, 92704192, 32226996, -28423872, 121744848, 58556580, 29594496, 9283072, 15120686, 72315336, 2826802, 15079968, 237658362, -329647280, 104566317, 33943680, 56123356, 47507064, 5614056, 55151104, -672452, 6981216, 151935732, -877568, 178905651, 91551648, 205287289, 31653984, -6853412, -85011072, 306062658, -78630528], "weight": 6, "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, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "field_poly_is_cyclotomic": null, "field_poly_is_real_cyclotomic": null, "field_poly_root_of_unity": null, "fricke_eigenval": null, "hecke_cutters": null, "hecke_ring_generator_nbound": null, "hecke_ring_index": null, "hecke_ring_index_factorization": null, "hecke_ring_index_proved": null, "is_polredabs": null, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp_display": null, "trace_hash": null, "trace_moments": null, "trace_zratio": null}