# Stored data for newform 6.15.b.a, downloaded from the LMFDB on 10 May 2024.
{"label": "6.15.b.a", "space_label": "6.15.b", "level": 6, "weight": 15, "hecke_orbit": 1, "hecke_orbit_code": 68971134982, "dim": 4, "is_polredabs": true, "nf_label": "4.0.78400.3", "trace_hash": 1450421651084570795, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+\\beta _{1}q^{2}+(-819-7\\beta _{1}-\\beta _{2})q^{3}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "b", "char_is_real": true, "Nk2": 1350, "analytic_conductor": 7.459738089114359, "hecke_ring_index": 23887872, "level_radical": 6, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [6, 2, [5], [1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [5], "field_disc": 78400, "field_disc_factorization": [[2, 6], [5, 2], [7, 2]], "field_poly": [51, -22, 23, -2, 1], "hecke_ring_index_factorization": [[2, 15], [3, 6]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.039", "prec": 17}, {"__RealLiteral__": 0, "data": "3.771", "prec": 17}, {"__RealLiteral__": 0, "data": "1.069", "prec": 17}, {"__RealLiteral__": 0, "data": "72.906", "prec": 20}, {"__RealLiteral__": 0, "data": "30.181", "prec": 20}, {"__RealLiteral__": 0, "data": "2005.406", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "14.2.3.c2", "trace_display": [0, -3276, 0, -1654072], "traces": [0, 4, 0, -3276, -32768, 0, 239616, -1654072, 0, -2153628, -11735040, 0, 26836992, -248212120, 0, 520179840, 268435456, 0, 908070912, -1252067608, 0, -2512164312, 2708779008, 0, -1962934272, -1010496860, 0, -18844787052, 13550157824, 0, -22159872000, 48544485512, 0, 126848191104, -73181085696, 0, 17642520576, -229361099608, 0, 176113271880, 96133447680, 0, -532172648448, -475123816024, 0, 78358129920, 1407078998016, 0, -219848638464, 546417874380, 0, 330389632512, 2033353687040, 0, -3372586813440, -6195118383360, 0, 6429522003912, 3954244177920, 0, -4261313249280, -8008506933784, 0, 13558362184584, -2199023255552, 0, -12945338929152, -5706498189208, 0, 6766877922048, 26012049530880, 0, -7438916911104, 28135799923400, 0, -21928288537260, 10256937844736, 0, -17912213729280, -80292052723192, 0, 35435631821508, 12944796721152, 0, 20579650043904, -16204620119040, 0, -46328672200320, -22190317633536, 0, 110399597015040, 120737034068560, 0, 53737779031272, -219496277852160, 0, 16080357556224, 178244166574856, 0, -158408610377472, 8277990277120, 0, 74911093899264, 120832025754056, 0, -524931158787840, -351933283454976, 0, 154376495529984, 629124457622120, 0, -217525729406328, -111002892894208, 0, 530252948901888, -329404253621760, 0, 222656103507240, 280072000499712, 0, 181533671424000, -1124120642251484, 0, 556853486697216, -397676425314304, 0, -129386444414976, 1618397291196296, 0, 403417966734216, 876882459648000, 0, -1039140381523968, -3081363876426416, 0, -1120164915968640, 599499454021632, 0, -2399932737183744, 1556275152329384, 0, 1947860564958720, 157911135805440, 0, -144527528558592, 2266875908225280, 0, 2750507322016860, 1878926127988736, 0, -2609191976048640, -3098034813453496, 0, 2144358221773824, 6023952503955456, 0, -1442719923240960, -14003819482783000, 0, 3008700655327872, -787525203394560, 0, 1443437857677312, 2233441064324456, 0, 3858600048710400, -4860834661920768, 0, 4359558336086016, -220024327481556, 0, -17029639636956504, 3892214300868608, 0, -1964870272512000, 15573278360643080, 0, 1073042592759936, -1766405978431488, 0, -641909800304640, 18344243145943592, 0, -11457484995136824, -11526791151747072, 0, 13379528678658048, 9426990839141376, 0, 9701702807458536, -25897852413911040, 0, 1801000046297088, -1315298159574520, 0, -34455900953260800, -4476255226920960, 0, 33682731487801344, -7051794249510712, 0, 33949041391491912, -9415525933879296, 0, -2706551869538304, -27195174810017280, 0, -48685911539618304, -16657233404231680, 0, 3178365699317760, 69656308246505192, 0, 25734564895760640, 45426703197745152, 0, 27628231175700480, -82342163195240816, 0, -36221086315333080, 50750409796485120, 0, -59141363949268992, 106749956448202376, 0, 75092339368207620, -4076044098945024, 0, -52670644256047104, -59489356614985048, 0, -68893796263686912, -32393168305520640, 0, -54619079166812160, -95355041554713600, 0, 76326691527952488, 20287823575154688, 0, 34908678138101760, -46753281525800824, 0, 114017569432075764, 65605688801558528, 0, -58255260530761728, 52403500838999440, 0, 274943605136605056, 55859760535756800, 0, -111070103016112128, -397669976337655296, 0, -52319398479989760, 18014398509481984, 0, -26861162197118976, 364823008197897424, 0, -99684801104636160, 125827158087389184, 0, 106048216507613184, -147298174831837440, 0, -382947630597944064, 46747633165991936, 0, 70971202007838720, 329499155719821320, 0, 152302382473746960, -93203222606241792, 0, -55434263937417216, -455596947593783512, 0, -332428645503564984, -213090709756968960, 0, 154694516563722240, 335711533312656680, 0, 270171314387631360, -117886292093706240, 0, 60939607335763968, 505360026117152644, 0, -353104305821880984, -230488472972492800, 0, 390911255193876480, -52185733531557120, 0, 308387109192762240, -419292646596857856, 0, 179636539697233920, 186954070255179472, 0, 179010000847504512, -84024834824077312, 0, -9659461917523968, 279145934768606696, 0, -497297544041138904, -654026409521848320, 0, 146736854870261760, -143796314905554616, 0, -530633683913356800, 657752495908388864, 0, 256402427396419584, -39634888860414720, 0, -592502093419284864, 249005842078973952, 0, -290288695881793536, 169201935947493800, 0, -591032039736552120, -106043774739677184, 0, -507214985250078720, -761981374521057112, 0, 1451489833228421736, 1587660768792305664, 0, -168588493159661568, 1251170568144345992, 0, 685998182956497408, 132748248015175680, 0, -628200340501192704, -1234007523739674992, 0, 1187270182407375360, -59299576999047168, 0, 379524482665021440, -2769174968608928536, 0, 1182791041156375560, 181783082053926912, 0, -457662879461265408, -1257181961076472320, 0, -1030905694519981056, -498743231023116288, 0, -904393498747207680, 2225802617190289452, 0, 2694132783348784596, -989077783089643520, 0, -2497584242838859776, 473931258607835912, 0, -728972964836540928, 2891088575345418240, 0, -440219885824180224, -1411362634731508696, 0, 1220223190465440000, 1798113508164894720, 0, 1307240932759695360, -1956398291118966232, 0, -3991888074999152664, -972766825574498304, 0, -131730289100587008, 3371117433886379520, 0, 208990833233039208, -1460176212581220352, 0, 1333029459712204800, 3535240995814643712, 0, -1166888012500073088, 834299653871628288, 0, 1297683336212250624, -70633535039220376, 0, 1499342408775411984, -67813296350167040, 0, 2937004902421106688, -3449892351085709360, 0, -4985894752263452160, -2483405846295306240, 0, -613671681222770688, 3355537478037029960, 0, 2126971623868579584, -989855954977226752, 0, 3329343601776304128, -13437125423527207680, 0, -3046361035232253816, -10832036969253052416, 0, 4300236052789985280, 9924458561401238696, 0, 5887903336883850240, 2883037458063163392, 0, -2096088722951086080, 15310618918065834832, 0, -7986837428385304320, 1315695822459985920, 0, -1264652251381628928, -1990423407641526136, 0, 2433473109608244480, -5153787556840407040, 0, 209525946667683840, -1001020891988792248, 0, -10770920394766558740, 4471021433663815680, 0, 1781970775296638976, 18708213032660897280, 0, 1399720350829940352, 909335698589351936, 0, 1218965896806174720, -11817247439517414912, 0, 5346716558536206504, -4980632962631479296, 0, -4343832157404266496, -7174284994507921720, 0, -7573342188395589120, 2698479645669457920, 0, -3116482027568308224, -10150188993724159480, 0, 13804216158247153920, 16113191168161456128, 0, -1823998799931310080, -17137689585232439216, 0, 7547660149104137160, -2294349828093640704, 0, -3626255087392370688, -20864010871134859480, 0, 9505507723791577344, 14048794101083357184, 0, -1487123836305408000, 16129694354339322640, 0, 9723162088030680576, 9208796301324156928, 0, -2709670568889563136, 1362581917839414728, 0, -5481404639881491384, -19102643829666754560, 0, -4561743763023593472, 8430028647303121920, 0, 7316496551618184960, 3257765276174778368, 0, -13529285105559810048, -449564030069963800, 0, -4568880306621604608, 15728523655899967488, 0, 1059933752647483392, -8753987635064259840, 0, 3552466180321058364, -13257910609480056832, 0, -8316911587649126400, -2858200838130913520, 0, 3230770261167565704, 28823495567703539712, 0, -3304799983486697472, 12490109689818792960, 0, -19794645418875836544, -7183421109436416000, 0, -6301488848455249920, 34132065709930591400, 0, -2367686967519386520, -49645352656441909248, 0, 8512638005444345856, -46770982291388089916, 0, -9535049267638825728, 25242532875685199872, 0, 30401345189106081792, 28986896595511699200, 0, 2985445973988199296, -29566775830457511936, 0, 9176390991615098880, -31561076793815405848, 0, -9678397766116875768, -4911099527345209344, 0, 35365464786943549440, 9749690458709031272, 0, 63333733514413636008, 41357650344900833280, 0, 19660248983009230848, 26164253826448521616, 0, -62307318809178950400, -12749006047882313728, 0, 5069643688123047936, 29415987902050331920, 0, -32915057958252739584, -78381385970858631168, 0, -15956873748141834240, -33519404976530826240, 0, -41934996590337708984, -1293608024518164480, 0, 15300890622881095680, 110542281599887505960, 0, -1313575159695869952, 26384305912210735104, 0, 1183969513951985664, -93353922686985495544, 0, -38666473603048914840, -18570247440181493760, 0, -12520162785972105216, 21913951364398861056, 0, -8363443401635212800, 29074058168814366720, 0, -22532155981962117120, 71827012047909063376, 0, 78847117299735525504, -15392162840483725312, 0, -7465799215822639104, 50384496352469207040, 0, 52222082313726353448, -81475051299312353280, 0, 21374500667790458880, -59001232205824225720, 0, -92833855300405202904, 25379101191811039232, 0, -346025879792603136, -31624927615659706744, 0, 77622938205129112320, 122081063597671342080, 0, -17566582552771166208, -24193823685837821272, 0, 17757835060551989760, -49348218912403095552, 0, -37375323203468537856, -76485892638554288728, 0, 148262482234010661120, 54793000136099438592, 0, 11818761611189944320, -65736322313447143100, 0, -16730360426164854528, 114719289202958336000, 0, -94208869004267888640, -205446611310701920696, 0, 31489680326002669512, -5343605879834259456, 0, -24647275768445927424, -48873635017545865800, 0, -19656852551999792640, 6451406466208235520, 0, -18163970624908136448, 225563565967534264424, 0, -60642360583428729600, 36845808061753884672, 0, -11824642930092539904, -74636521028727996672, 0, -18152480665663260336, -18296349198945943552, 0, 29199811307663462400, 57118666174792761600, 0, 28022177969994316680, 107464236533002567680, 0, -31609651599035596800, 81888528345968546600, 0, -26785833047154754560, 39819957550454931456, 0, -26267888754966749184, -136391222227256363520, 0, -72546208418090323224, -143453598689860362240, 0, -35713501889216643072, 264729937573141766408, 0, 15995116410793056180, 1802439290728906752, 0, -44657485678289240064, 64236302768749927312, 0, 211635267299413414272, -139861128236682878976, 0, 139506807905947680768, -103997644956955952640, 0, 169773791822178154632, -31885019552715636736, 0, 83026034644451328000, -77268832007791679512, 0, -152818237047201836544, -90312302766644170752, 0, 16096217272418304000, 43913879908498888704, 0, -218524570711297940736, -127576296330388111360, 0, 208665178022761574400, -305511390069829608944, 0, -143700471929679436800, -37608072627237715968, 0, -8790364919889395712, 57842182796667521960, 0, 8610672091607240904, 14470397775310749696, 0, 47936573081784188928, 390113011822173120000, 0, -228266065578795821568, 92113253654904004608, 0, 5258525084095610880, 215325634929979919632, 0, 20457349863665429736, -150276039851569905664, 0, 131290210509186852864, 151358610706266628424, 0, -257282670058749227484, -10434400656883261440, 0, 93859717080160862208, 9894667189484419304, 0, 327297330429339150720, 94427473115112013824, 0, 149143205156623589376, 218766292752302766440, 0, -369752483224542141360, 166730148055369801728, 0, -109605098935566729216, -68745730837631535360, 0, -1342832837157358848, -77225908954246152192, 0, -164876746302238924800, -704563913685164014840, 0, -458840330821656971136, -251333541318872064000, 0, -79476349398700326912, 486319884688575109160, 0, 889437455085702910464, 212155206974759239680, 0, -201690646341228343296, -209685400910255948720, 0, 223600739107547980800, -120910221768359018496, 0, -14753792379265744896, 193151654370701961224, 0, -101427109676037955584, 10774922523234467840, 0, -108771158533117796352, -378703129109587265080, 0, 90564970049095795344, -64677337997171822592, 0, 282262740609112473600, -456611829702995427840, 0, 403469900250281838720, 36669482818936504320, 0, -85002473542021410816, -272785316022383407384, 0, 250088849657793812736, 177732250694805872640, 0, -275928936348068610048, 581269117191186271120, 0, -231986200886283029760, 57768298491991752704, 0, -299307017527444168704, -482308673899235512320, 0, 273914988821606748672, 657264680778580574208, 0, -278110547079101743104, -474832485579145559040, 0, 863975908181709470592, 77131988450339192832, 0, -328112190488194191360, 1108083732318074061224, 0, -469986525577672692120, 593611612779717648384, 0, 22172072915257786368, 162023827239866084368, 0, -887891044121191721520, 222782872043661557760, 0, -29388932968765612032, -1467851706893266097080, 0, -128790843570481484160, 36222271257992945664, 0, 398834987332553146368, -37972470613612209688, 0, 16590026473595349768, 136456056047465922560, 0, -105211322048003272704, 224583289925334658560, 0, -274860988870078189656, -490203332060351508480, 0, -26037171808811089920, 678952617037123392484, 0, 437909039521273287936, -570624477155370532864, 0, 200317267520364625920, -716292213169100426488, 0, 87373787671998099720, -40207578219415388160, 0, -210817555626071162880, 57243912917827879208, 0, 671770862963827683840, -372135552595928285184, 0, 743781307643618549760, -211437323647325874904, 0, -291258904554434492928, -352669045094952321024, 0, -226330469791338332160, 967058990827648830720, 0, -346998736845414060876, 674547000895412764672, 0, 616279915992139038720, 217096540657066679440, 0, 582564857215745667528, -1601597715689077850112, 0, 296723139095208591360, 119098252043438390888, 0, -558420756728621339520, -415747357052806103040, 0, -79501259238724915200, 1305863897581460346344, 0, 232535349641353086720, 1076464347326333054976, 0, 484486053472411582464, 1106599770816341306512, 0, -1977250140915573468672, -874495643223673864192, 0, 465282798881927491584, -146287854641443265280, 0, -331917147425451594240, -463106774014469406720, 0, -615156444104356823040, -775953678028708703232, 0, 300282845045450278032, 33390953258557636608, 0, 129071039722474622976, 1608326502078586781864, 0, 198322464114688161024, -1728703346261890252800, 0, 431477917745537875968, -3547230687785907355392, 0, -2485016177845700862720, 487336809389957513216, 0, 337377024009324085248, 1256665165623784722248, 0, -1334700526841175493944, 2881081873636096512000, 0, 564377978992123183104, 1646726596802715417320, 0, 1239892304081341594248, 265364834758825082880, 0, -124221484283426611200, 2805560775572425798200, 0, 1423245692281513510656, -1417582147276170326016, 0, 447439496534525214720, -2807377106882649634360, 0, -1208570349305282578776, 781148500416213811200, 0, -1278089219113688494080, -1805755231066795766784, 0, 2609706501700332491520, -348155300298904117248, 0, -625268256996986781696, -1684239223007377415600, 0, 2193225141407659005312, -166197850727667204096, 0, 293761475768645332992, 63343729094648647680, 0, 1221625037915637868800, 1304090008800435535872, 0, -285971891307329617920, -933065966722947413748, 0, -1110934723073126692608, 383002882259360350208, 0, -1048298193493449228288, -2591006120244035975992, 0, 1146380094681993133056, 610447802218138951680, 0, -934031928787564658688, 536452154085067008208, 0, 1280359677894866641800, -537441802662367461376, 0, -275256184201081122816, 6676087876777702614528, 0, -90472650954291351000, -389602992074443640832, 0, 477227094268000075776, -3851529759798045707520, 0, -3828615552881915765760, -429289478873083412480, 0, -1329056529088044072960, -632186110383312866680, 0, 1018881301678771369608, 1244562731759808921600, 0, -2252338013279068618752, -307447906949591540056, 0, 1280695631600712978504, -457603158308919705600], "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, 3, 2, -1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "6.15.b.a", "char_is_minimal": true, "conrey_index": 5, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [-819, -7, -1, 0], [-8192, 0, 0, 0], [0, 351, 38, -19], [59904, -811, 32, -72], [-413518, -111, 148, 259], [0, -8192, 0, 0], [-538407, -28341, 1170, 1053], [-2933760, -912, 1216, 2128], [0, -85071, 12830, -6415], [6709248, 57344, 8192, 0], [-62053030, -780, 1040, 1820], [0, -406414, -37888, 18944], [130044960, 691635, -28554, -25785], [67108864, 0, 0, 0], [0, 2236668, -17912, 8956], [227017728, -514071, -172224, 117936], [-313016902, 155127, -206836, -361963], [0, -2875392, -311296, 155648], [-628041078, 16150357, 569362, -350649], [677194752, -307920, 410560, 718480], [0, -43220418, 1492132, -746066], [-490733568, 6643712, -262144, 589824], [-252624215, -653220, 870960, 1524180], [0, -62003110, -266240, 133120], [-4711196763, 102870324, -47223, 270459], [3387539456, 909312, -1212416, -2121728], [0, -120388323, -1523374, 761687], [-5539968000, 129448272, 4214208, -2881008], [12136121378, 2683845, -3578460, -6262305], [0, 67108864, 0, 0], [31712047776, 398620941, -16155282, 5951907], [-18295271424, 429888, -573184, -1003072], [0, -788334318, -29282324, 14641162], [4410630144, 232169472, -9584640, -8626176], [-57340274902, -11636436, 15515248, 27151684], [0, -322945030, 52950016, -26475008], [44028317970, 527519590, 63148150, -2464020], [24033361920, 7471104, -9961472, -17432576], [0, -405730710, 56996612, -28498306], [-133043162112, -643816742, 26663488, 29773296], [-118780954006, 410247, -546996, -957243], [0, 696901632, -105103360, 52551680], [19589532480, -3331303389, -115835130, -6505839], [351769749504, -35811168, 47748224, 83559392], [0, 6692871900, 29988840, -14994420], [-54962159616, -469762048, -67108864, 0], [136604468595, 91800996, -122401328, -214202324], [0, -210818135, -222965760, 111482880], [82597408128, -2274132852, 90327240, -160798284], [508338421760, 6389760, -8519680, -14909440], [0, 10733013003, 38071838, -19035919], [-843146703360, -4702164291, -33107616, 5254632], [-1548779595840, -34883028, 46510704, 81393732], [0, 3329343488, 310378496, -155189248], [1607380500978, -16334303153, 95218594, 490046193], [988561044480, 36560976, -48747968, -85308944], [0, -8598314571, 273042214, -136521107], [-1065328312320, -5665873920, 233914368, 211230720], [-2002126733446, -517172004, 689562672, 1206734676], [0, 11964355298, 916085760, -458042880], [3389590546146, 4071508299, 486456696, -1099860363], [-549755813888, 0, 0, 0], [0, -26300323530, -2453362340, 1226681170], [-3236334732288, 32031751056, -244875072, -972719280], [-1426624547302, 840366747, -1120488996, -1960855743], [0, -18322784256, 146735104, -73367552], [1691719480512, 73387614342, -2945315580, 3091726314], [6503012382720, 702775776, -937034368, -1639810144], [0, -5260134918, 2352370636, -1176185318], [-1859729227776, 4211269632, 1410859008, -966131712], [7033949980850, -378277776, 504370368, 882648144], [0, -56595542998, -3971903488, 1985951744], [-5482072134315, 79776555125, 1169745095, -2063521980], [2564234461184, -1270800384, 1694400512, 2965200896], [0, -183428926746, -2173410212, 1086705106], [-4478053432320, 43444284130, -1705346240, 4467818160], [-20073013180798, 303345813, -404461084, -707806897], [0, 23555211264, 2550136832, -1275068416], [8858907955377, -44721850734, 8285513652, -7670399490], [3236199180288, -1367918688, 1823891584, 3191810272], [0, 144414004035, 20943453402, -10471726701], [5144912510976, -132303724544, -4664213504, 2872516608], [-4051155029760, -1882824624, 2510432832, 4393257456], [0, -118807209814, 140030976, -70015488], [-11582168050080, 58496405145, -2257453758, 8688524805], [-5547579408384, 2522480640, -3363307520, -5885788160], [0, 60399863214, -34631630756, 17315815378], [27599899253760, 20308026672, 4539471552, -8548316208], [30184258517140, 7210430370, -9613907160, -16824337530], [0, 354061664256, -12223545344, 6111772672], [13434444757818, -405460303391, -15904239758, 8478266355], [-54874069463040, -719732160, 959642880, 1679375040], [0, 789014468898, 7068082204, -3534041102], [4020089389056, -54425288704, 2147483648, -4831838208], [44561041643714, -5945558604, 7927411472, 13872970076], [0, 130729204851, 31334739968, -15667369984], [-39602152594368, -1020098811339, -4048290306, -26205950331], [2069497569280, 5351178240, -7134904320, -12486082560]]}