# Stored data for newform 38.8.e.a, downloaded from the LMFDB on 16 April 2024. {"label": "38.8.e.a", "space_label": "38.8.e", "level": 38, "weight": 8, "hecke_orbit": 1, "hecke_orbit_code": 275012124710, "dim": 30, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [108015819711838162868595539904165656250967023561, -1948562379986117946477475735027697991686158779, -920305414221285359849156193095037316395171279, -24737284809001567901455245281309092809869178, 5911376741936935856134404356037752378256591, 178517371100498660441664077130273578849334, -3137634193461150141428473657175175582327, 59666402686798164188393216339202588861, 3775275320370694395193691151369891354, -476332564825651509811060785392312034, 12795882701177500973973281482449147, 21610894875993578628194432802156, 13988370656557996601704121378475, -479561465752913822004208703952, 30418458673722866791326259965, -840367814984801045159355468, 27195236446305820756025538, -341741557472170193374005, 8990773890506815548439, -29532229649838801783, 1221203031052371795, -15472915269304860, 504083095624827, -2972803849713, 77537897434, 302810589, -5241915, -99603, 2565, -45, 1]]], "char_order": 9, "char_parity": 1, "char_degree": 6, "char_conductor": 19, "char_orbit_label": "e", "char_is_real": false, "Nk2": 2432, "analytic_conductor": 11.870630968396627, "level_radical": 38, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [38, 9, [21], [8]], "inner_twist_count": 2, "level_primes": [2, 19], "conrey_indexes": [5, 9, 17, 23, 25, 35], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 5, "sato_tate_group": "7.2.3.c9", "trace_display": [0, 45, 0, 1806], "traces": [30, 0, 45, 0, 0, 360, 1806, -7680, -3105, 0, 9786, 0, -11130, 6144, -1818, 0, -65250, 29040, 105906, -47616, 172854, 102336, 101004, 23040, -132756, -92112, 43659, 96384, -273912, 0, 58710, 0, -406965, 84960, 356100, -198720, -2598852, -219336, 1769844, 0, 43377, -79056, 1126698, 818688, -912546, -530880, 588306, -368640, -2778285, 1665288, 3972045, -430080, 6520866, -486648, -1666818, -1849344, -6947844, -4573152, -970467, 4634496, -4037670, 755952, 7946472, -3932160, 1497690, 6499272, -4817025, 1472064, 10299876, 2848800, -25171290, 3179520, 1347750, -3123936, 8817984, 1583232, -11476764, -930960, 10777986, 0, -5365035, 347016, 9745314, 877056, 29258556, -9338208, 25598802, 5010432, -20353740, -30112128, 19748724, -14097792, -18738174, 12376608, -20427204, 0, -23005029, 14869008, -45819771, -15915264, 72315294, 27254496, -12366342, 9139200, 27990540, 10745376, 63588453, -3893184, -109061364, 9526032, -96479646, 6168576, 11655444, -36070056, -31048224, -17530368, -7894842, -11075016, 8136276, 37075968, 40474077, 18712128, 95990946, 11039232, 89797806, 42295056, -29363130, 0, 116254173, -94853568, -24352842, -36362880, -231225858, -3146784, -141097356, 27970560, 68185677, 10738896, 36872049, 10947840, 159273606, 68419296, 286195770, -7434240, 78088620, 10782000, -92614875, 14571648, -75704136, -7102512, -204511188, -37180416, -233275830, -251235984, 65305044, 131304960, 121216794, 86223888, 160688802, 12189696, 17524374, 254521440, 167043696, -2382336, -180732168, -92112816, -41613150, -83441664, -290868330, -135027744, -561277917, -139467648, -878019042, -85062864, 745109436, -41422848, 404448336, 139392936, 389877918, -65200896, 520947552, 255183552, 119958420, -112782336, -281079810, 209391168, -428756484, 37651584, -106808880, -561113472, 377825580, -23592960, -252542154, 473638080, 268189848, 118952064, 277249248, 339224760, 355365678, 195293184, 336030063, -72219936, -1043889972, -176754624, -85914444, -305718672, 774883068, 94322688, -1007166630, -519805440, -2506771152, 57744384, 1315999680, 29080944, 620012592, 22353408, 702915930, 302536128, 2246006445, 216892416, -482692074, -771837168, -1048473786, 25165824, -241873137, 711407400, 442555092, -154653312, -1597196604, -1000885536, 8756280, 77411328, 370233615, -63158736, 592329348, 105222528, 34505340, 562342512, 1177533768, 0, -1423072695, -348260808, 675083754, 189197568, 951371958, 288568368, -1174141062, -60119040, -1460017392, -137031984, 851071581, -179735424, 216959820, 235966704, -352793124, 0, 1544587968, 1034532192, -1015582200, -758828544, -2152266510, 809285160, 1000841280, 415953408, 3536237868, -151207776, -4386255384, -308289600, 1847443212, 796260528, 13400838, 223764480, 644852508, -234561600, -367320105, 106232448, 2298433596, -101709840, -4308008538, -783200256, 1382371119, 513740160, 2062228539, 139448832, -1292904324, -3938112384, -4377580236, -101744640, 2154539910, 111006912, -339312909, -145694976, -1695513204, -257554992, -690528354, 665306112, -546547581, -605633088, -1940009472, 1090259136, 5874138468, 3255057552, 3791526036, -136114176, -3673223220, -957296328, 2602672632, 1246835712, 1613389314, 522440352, -368988858, -453080064, -2990328036, -1907388960, 4014040428, 424368000, -6466283934, -4086942000, 5377203888, 0, 1643634654, 2798641536, 405892839, -2970006144, -2351763330, 2602401768, 2435475762, 16149504, -1889274138, -1400023872, -3644845602, 1001762112, 345708468, 208838928, -2244112512, -667533312, -3865996227, 1920292032, 10734184974, 1872547584, 633872868, 3083256768, -9133851528, -597645312, 3575757978, 3387990144, 5674845438, -680502912, -1333134126, -275504784, -3013364340, -87785472, 4654272528, -844609800, -12593126724, -1865114880, 1911194088, 3015808056, 6496685910, 934447104, 3613438164, -10759990080, -6011933073, -251917824, 1810055454, -738542640, -1047506298, -271810560, -7193662218, -1126496736, 2038837248, 649516032, -5337979644, -3430051872, -2733695460, 212296704, 11725954434, 7612148016, 15221515392, 3898019328, -10901759076, 323322960, 1701259926, 94371840, 6019602678, -2020337232, -984408585, -1347115392, -2481743010, -3101560416, 7201360860, -1422481920, -15828135393, -6496966944, -10412356764, 1499884608, 8755226298, 4417617024, 5110328730, -1705254912, -9600331857, 920774184, 9855185604, 958707456, -11448844074, -4149658560, -7383220740, -619650048, 10425747435, 4895212992, -12961246146, -2445749376, 3270698538, 4337799600, 21190439730, 584908800, 16082235534, 7254259584, -7677708294, 1791394560, -1385055672, 7097537808, 999786114, 461955072, -1872942711, 720845808, -16161393948, -3141619200, 8002163568, -5798255664, -22245504552, -870248448, 7575704778, 543980352, 13560542640, 853539072, 4365735450, -11292163824, -19068055386, 243744768, 12929408460, -4032401088, -4809439371, -1181149056, -9117513312, 1403016816, 11806626318, 473432064, -6326980032, -1934985096, 4964635068, -18164544, 19867158318, 10444979016, 8219329608, 4144478208, -1588888320, 2841729312, 2343851337, 4855421952, 4141498524, 70050240, 812873718, 1170726912, -19876090518, -2733851856, 8815386306, -2313345792, -19829096112, -5197380000, -10790266680, 1205680128, 10563412767, 2588448768, -12048212322, -15112326912, -15738715986, -5399284080, 5397443304, -59572224, -6875772048, -8451901200, -8858446632, -234287232, 9740949612, 1425282264, -7265428686, 1513580544, 13144178958, 21870058128, 16928645646, 6143420544, 10085310540, 2571789840, 9263742948, 706510848, -1220305782, 9979839384, 15960990543, -1096255872, -1195797648, 2332812480, -4819192500, -2630710272, -1161222624, 2014567248, -3083018529, -3660256512, -13235964936, -14431621392, -7070536080, 4026531840, -10651690263, -37271233824, -16653986904, 3816098112, 13289103960, -12060456672, -10160984508, 766817280, 6588543786, 7441982256, 10289753340, 2579094528, -2170784082, 8006730240, 9389442510, -1666928640, 11572375356, 12072511536, -7665423222, 9256406016, 21538461864, 11798728368, 7770154824, 2009613312, 10879692465, 14779545696, 11315734674, 6280384896, -20264971998, -6215459760, 14861621508, 753696768, -21259992354, -33700895280, 13612167330, -14474756544, -21405287790, 1542150816, -2694969234, -10547073024, -34009597704, 10074952224, -8150824080, -3192793728, -6119525334, -16690878144, -2634655818, 4807016448, 19301947209, -3751474368, 6062915862, 4109921280, -6080305302, 17742437160, -7768053798, 4378834944, -12813925098, 5733887184, 13510018536, 18316529280, -17155523928, 12281809392, 5956082436, -813957120, 29530048224, 14961343200, 38364020430, -9145792128, 501638040, 15356089128, -14818384674, -9685541376, -4485807414, -29972974560, -26073163752, -11709556224, -47022992004, -32129285952, -15403810914, 666869760, -4113114003, -20151774816, 29806547148, 1961389824, 2952974436, 18417815424, 23131872654, -2257403904, 2306958408, 46993107744, -10554488055, 699145728, -9972073464, 19176466320, -1313894256, 810614784, 65256127104, 19542148128, 19020777396, -138880128, 7108901388, 20821381056, 25721542530, 2938051584, 33660515391, -26415443712, -5949752463, 11944448256, 8012859708, -42054011808, -21827659320, -7926865920, -25690744164, -20745663936, -54987889968, -39383834880, -19938416688, -333513216, -41081455698, -6792827904, 49623698409, -9885292320, 16579574460, 31283098368, -9170582058, -17234398416, 32552186730, 0, 1275139548, 39576789624, -26147813475, 1121559936, -3241044360, 8022729936, 60241439028, 16289372160, 5908605783, -15484950480, -2224664292, 20819214144, 16920582528, 35181085104, -2432177112, -306868224, -5476229931, 13014795312, 6058074018, -17403345792, -10248328170, -68968595232, -60197569674, -9979201536, -49912793850, -49000027680, -35955460596, -10691642496, -92410698426, -31159524864, -745918704, 449052672, -4183067877, 30780613776, 43279377786, 2528473536, 42310027716, 85873479792, 60146473410, -348020736, -34747944513, 27194294400, -40199945694, 26224578240, 34216943508, 57647365728, 2497667028, 4614955008, 9682338360, 28606063824, 40426472367, 20003721216, 12340403352, -69290216568, -31936447764, 13106586624, 54874934571, -59616779664, -39107962482, -46716247680, -60255683322, -23991810240, -72812577138, -5130682368, 51659912898, -21361464936, -63007512204, -10280212416, 20420732712, -19056844032, 12843402432, 25342033920, 50592210618, -30659486112, 17460289800, 24126464448, 100793460534, 62424768096, -8052941100, -4172857344, -81483330528, 50545637376, 182813510388, 33340643328, -29554664838, 11176149480, 13983650742, -2015342592, 22569739878, 58652899536, -15967352688, -49196059008, -17627040150, 20108637552, 37114155522, 3309699072, -84903114732, -126183522504, -117133473375, -57688834560, -18396073410, -35921725824, 62978134446, -3807089664, -11992181820, -88160821776, -75026617653, 5769192576, 1723273908, 62531430912, -615836790, -3168411648, 808205916, 93807635472, 87444762264, -18522307584, -201653484, 9364280832, -62809764612, 17608866816, 274327318188, 118260141360, -2291537964, 9476911104, 8012930760, 13610079408, 3571173336, 0, -13517595582, -76690331136, -72712892526, 17144187072, 120792476760, -37589483952, -48186225798, -18534262272, -155149081194, 12988042560, -20766287082, -33768451584, -13060049976, -13393530288, -45646630026, 1578369024, -19933212576, -85963586496, -18559613334, 32984802432, -11581757934, -41914498080, 16351369062, 11999076864, 155049645456, 49499047728, -65265999660, 22743403392, -63160397964, 64133125920, 197145168804, 12498763776, -80331110967, 8839243032, -57007038675, 7366193472, 39107750940, 21611068608, -72950902998, -44695090176, -122775334080, 10986742800, 74089094244, 34295137536, -106558281942, -106699640112, -105755226192, -27908603904, -22817420340, -7345542624, 107940445536, 9930674688, -66114837174, -63351326352, 35077067004, -6331567104, 7220328903, 2343039744, 68292433419, -18600285696, -976546266, 169523517840, 183713876604, -1761607680, 59669899026, 49726480272, -44764719144, 72953276736, 210869099100, 70851277632, -60936399474, -4030101504, 143393275722, -11080445376, -76854090066, 14324659392, -129731843184, -67066458480, -39929036484, 5501632512, 36188866272, -60569854224, -171367767960, -30794285568, -84358678524, -39336065280, 95694587370, -65114575872, 36272484798, -45067602720, -94151790291, -15259269888, -160804523538, -56429330304, -47284129944, 8955297792, -19553876124, -88922762592, -28893197304, 4351842816, 155444725098, 39496782816, 93770425080, 19362312192, 9787837932, 72816661872, 290359113888, 143744412480, -41061804378, 14875389024, 40996492416, 1949958144, 21246884796, 45837052200, -61010801949, -38075496576, -49696057314, 18715736544, 64543086396, -942108672, -44324662800, -35116513392, -75301221192, -55466115840, 60124359582, -65208565056, -937578330, -4768923648, -220712273790, -74264839128, -51764803584, 23698539840, -53196310758, -48063758424, -46176902808, -2983793664, -81880951110, 158937266544, 240798635541, -86210091648, 134910564246, 105615007872, 16397451588, 36327776256, 170804115774, 162265111752, -28862687304, -19959674880, -127573339152, 18750810696, -10339784820, 7948345344, 59431436391, -80027630160, -90957743940, 1659859968, -57709974438, -67631305104, -54325739628, 4021223424, -68780950065, 28910990304, 125493086358, -154616425728, 156304460544, -63524347752, -58862609670, 55270339584, -6080185113, -99349906464, -89011584906, 83803432704, -74117599494, -408598464, -123685333440, 9645441024, 4576328226, 155077756968, 82866075132, 2208341760, 43198585584, 53268530112, 95712408840, 35989920768, 24924845148, -69975028560, 118333210896, -43194272640, -83742043200, -10630375392, -123701882400, -18506317824, -54310192539, 26827485120, 49138379625, 65249080512, -193338075786, -94271352864, -46588304352, -41445454848, 169000172841, -46670328576, 222323396586, 8996605632, -28400882028, -237262102512, -59562346806, 9580609536, -70571228700, -1863865032, -193721345637, 3019011840, 63764086578, 135429165168, 11298842046, -62011709952, 111219993786, 103727183616, 101344812792, 132245617920, 210118586040, 138286947456, 65452393290, 3096379392, -37095417201, -9762446256, 78720376272, -20612683584, 30526284588, -100221377784, -597558456, 45976476672], "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, 19, 5, 1, 9, 0]], "char_orbit_index": 5, "prim_orbit_index": 5, "minimal_twist": "38.8.e.a", "char_is_minimal": true, "conrey_index": 5, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "qexp_display": null, "fricke_eigenval": null, "atkin_lehner_string": null, "hecke_ring_index": null, "projective_image": null, "projective_image_type": null, "field_poly_is_cyclotomic": null, "field_poly_root_of_unity": null, "artin_degree": null, "artin_image": null, "field_poly_is_real_cyclotomic": null, "artin_field_label": null, "projective_field_label": null, "hecke_ring_index_proved": null, "trace_zratio": null, "hecke_ring_generator_nbound": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "hecke_ring_index_factorization": null, "trace_moments": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null}