# Stored data for newform 21.35.h.a, downloaded from the LMFDB on 16 April 2024.
{"label": "21.35.h.a", "space_label": "21.35.h", "level": 21, "weight": 35, "hecke_orbit": 1, "hecke_orbit_code": 481623539733, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1588732807226003202, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [0, 1]]], "qexp_display": "q+3^{17}\\zeta_{6}q^{3}-2^{34}\\zeta_{6}q^{4}+(-253015451951165+\\cdots)q^{7}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 21, "char_orbit_label": "h", "char_is_real": false, "Nk2": 25725, "analytic_conductor": 153.77387348963694, "hecke_ring_index": 1, "level_radical": 21, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [21, 6, [8, 10], [3, 2]], "hecke_ring_generator_nbound": 4, "inner_twist_count": 4, "level_primes": [3, 7], "conrey_indexes": [2, 11], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.071", "prec": 17}, {"__RealLiteral__": 0, "data": "1.955", "prec": 17}, {"__RealLiteral__": 0, "data": "0.811", "prec": 17}, {"__RealLiteral__": 0, "data": "17.617", "prec": 20}, {"__RealLiteral__": 0, "data": "10.554", "prec": 20}, {"__RealLiteral__": 0, "data": "214.633", "prec": 24}], "related_objects": [], "self_twist_discs": [-3], "cm_discs": [-3], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "34.2.1.d6", "trace_display": [0, 129140163, 0, -457653465545653], "traces": [0, 2, 0, 129140163, -17179869184, 0, 0, -457653465545653, 0, -16677181699666569, 0, 0, 2218611106740436992, -13257178113610601474, 0, 0, -295147905179352825856, 0, 0, 10533550932831642194149, 0, -38921926981395836058246, 0, 0, 0, -582076609134674072265625, 0, -4307387926151115532621494, 5177890428476387049340928, 0, 0, -19599701438028304062305147, 0, 0, 0, 0, 573023599916140863676219392, -859594323581411974757802287, 0, -856017071255852796440200131, 0, 0, 0, -17470096463040699199417500122, 0, 0, 0, 0, -76230897167940336331108909056, 101212782450041974235107874711, 0, 0, 113878292870409011619438788608, 0, 0, 0, 0, 2720608968869360649020159012574, 0, 0, 0, 4468002075713925041487910419766, 0, 2605986005735392637396581440459, 10141204801825835211973625643008, 0, 0, 22022844874719432605769728964013, 0, 0, 0, 0, 0, -20073068910160542409412259436943, 0, 75169468182139098644256591796875, -361930054138097567182749100408832, 0, 0, -336858662185559380928110634527811, 0, -278128389443693511257285776231761, 0, 0, -346681447768257186026240461504512, 0, 0, 0, 0, 0, 0, 3033596753524937217268086468046261, 0, 2531108638458309585219648839318961, 0, 0, 0, 4155647952096798288265379422464004, 0, 0, -10000000000000000000000000000000000, 0, 0, 27373599664373738833789028549196517, 0, 0, 0, 0, 37000180548008608733053875753320448, 51939534252863995924692174245206129, 0, -222016302122356572380748945729905562, 46119981443560569174740502069641216, 0, 0, 0, 0, 110546184112763444836293264669961353, 0, 0, 0, -255476698618765889551019445759400441, 0, 0, -336720306750782946679778210949890048, 0, 0, 2082896459099234320004587663670723974, 0, -1128045552431399685123372735403799943, 0, 0, 0, -1645978728061053068339610037507767839, 0, 0, 0, 0, 0, 7341316230638264239621616368781558902, 0, 0, 0, 0, -4922235242952026704037113243122008064, 0, 0, 10824082244945691244684153212615526251, 29535436060875248200700306747992047616, 0, 0, 16517579415780494756203584790134693406, 0, 0, 0, 0, -14706261303446357637203219129359663104, 11254642014194441892174472328255779318, 0, 0, 0, 0, 0, -12959265145171043492871348686855022458, 0, 0, 0, 0, 0, -61783005388574183145293103304263938640, 0, 175669942849525579960124562584862704781, 150066985933450151556943090548132020224, 0, 0, 175433751607687445357441902160644531250, 0, 0, 0, 0, 0, 853638633008574144979801377000998685694, 0, 1153997032684069242455061028275959323716, 0, 0, 0, 0, 0, 985645505926280640593840953149113032791, 0, 0, 654818420562085528442706783619516465152, 1341305752258955080594940873019155291761, 0, 0, -1439957273439588432052140801390719008768, 0, 0, 1211251828089963319070660303438569869694, 0, -2844033776844982105976617538878459954119, 0, 0, 0, 0, 0, 0, 1956414174410866684196694379780869455872, 0, 0, -7245005972525165246492894019418451639372, 0, 0, 0, 0, 0, 5907210665578117753222397495352971062774, 0, 2592239390968364802919911917885107241709, 0, 0, 0, 29545513201350568834040621154345165266596, 0, 19414794747329513775184750556945800781250, 0, 0, -23369853092996372167941834807449965559808, -2135551447834293793302892748814336020351, 0, 0, 0, 0, 0, 0, 0, -87003965085210149398470597249909881146386, 0, 0, 0, -61215781142871334005999250994478446660834, 0, 35917545547686059365808220080151141317043, -153519382349211391239888147458180815781888, 0, 0, -69822580442669090868080247589212486787813, 0, 0, 0, 0, -131123118170533811027278226768256709951488, 0, 0, 0, -87112285931760246646623899502532662132736, 0, 0, 134320703473988480172758834232062744673757, 0, 0, 0, 0, 0, 0, 0, 0, 378349594007204720869828187228879183675392, 0, 0, -458630726138836901517853499016558861527282, 0, 257997459258655410983237866222212678727302, 0, 0, 0, -661577257396631107408600659676711456885487, 0, 653735564282428337079455683824822865061286, 0, 0, 0, 637562141703315276171515172567304486009477, 0, 0, 0, 0, 0, -684326450885775034048946719925754910487329, 0, 268330526952198361362356042936923669096326, -344852697997975567032186787452550236864512, 0, 0, 0, 0, 0, 0, 0, -2582803260000000000000000000000000000000000, 3997625094863715484991845776365489962034833, 0, 0, 3108955491925277037414140483258707339116544, 0, 0, -842330366761864841342371760250434524141178, 0, 7070062245107939851829890108909783448824542, 0, 0, 0, -1563295752521508014760500130413937990315959, 0, 0, 11574375499690315396417930418934053179752448, 0, 0, 0, 0, 0, 0, 0, -4778209346999261057189801002565550445953024, 3858346641532436907873488962650299072265625, 0, -6707479919558939650546083106850321467659027, 0, 0, 0, 8166587094350406828180925009307788299095701, 0, -14335610722369186850685608456819079125643303, 0, 0, 17443667135281099783787763930963424296566784, 2524039328736162056750150979612648934818382, 0, 0, 0, 0, 0, -21553568170229422464007591556311803168441886, 0, 0, 0, 0, 0, -59596520479083210433387502613520835590829804, 0, 28551904470700563293200841030561900660241078, 0, 0, 0, 0, 0, 0, 0, 0, 0, -80921055143577981823283230454324330280522480, 0, -65984605004658603670917296083077263466023766, -34322107831535488927838687631615472682663936, 0, 0, 8659181381447503420847351238951788508411229, 0, 0, 0, 0, -86968230598412220223693733931834371261595648, 65464294111750389614189693149676573271778297, 0, 0, 0, 0, 0, -62415164576911588042868592054049036320457178, 0, 134492794120098976630293305817113236165183881, 0, 0, 0, 0, 0, 145675986512416001654981030159802595458410709, -35696744095890246548817170377028529834426368, 0, 0, 0, 0, 0, 0, 0, 0, 97878224913460749647798473099848674594308249, 0, -622548061498824239524598936587633247299020411, 343597383680000000000000000000000000000000000, 0, 0, 129918366468765532538660392624905660797993339, 0, 0, 0, 0, 0, 467759765774212617366300362853387350620776049, 0, 0, -940549722658254276898952459059274940736864256, 0, 0, 0, 0, 474029387329585518970903298093959313999190513, 0, 0, 0, 1296713806351348248147937381160298326427522958, 0, 0, 0, 0, 0, -698172574514791504117403965782407990284972226, 0, 0, 0, 0, 635658261599169329739705562266234750272274432, 2201341851135939774640526927979962598993170158, 0, 0, 892314403942090627329720669001175235335028736, 0, 0, 1617727257044978782428359994867405783333331294, 0, -290120217810481204194328170750853018542317646, 0, 0, 1907105513588753737651947163792846475917000704, 0, 0, 0, -2320578761181905317504705862527254487852122112, 0, 0, 0, 0, -2133082898119337865036776200982315098405865178, 0, 0, 0, 3106632694260330874445889422298380126324501713, 0, 0, 0, 0, 0, -7835760998689731163739529836693637272556664394, 0, 0, 0, 0, -3798337963695310174049437164980449957751291904, -6637528869592934344136548859205948971309689946, 0, -1453426304219718539649439780909940846818548834, 0, 0, 0, -12262667218260050511626759544014930725097656250, 0, 0, 0, 0, 0, 5697897526583702083208044032993054650221385519, 0, 0, 8778112523661182940015813143973366229303820288, 0, 0, -519467725506344636142196314727817255484534491, 0, -3347123226415214439098990614900587115189561308, 0, 0, 0, 0, 0, 0, 11569621643149606227073273604505334807646961664, 0, 0, 14700254972041861601335451970204449720061003949, 0, 0, 0, 0, 0, 0, 0, -3989333693255174174487502021744241815495799160, -17891944345570826046121005170861613561946308608, 0, 0, 6049880256181769920181965769528312304857407006, 0, -22686045053788417868720019512512871028039219303, 0, 0, -19379675024364459724438334495109528437246656512, 0, 0, 0, 0, 0, 0, -7089561054746234681081680217404159924458158819, 0, -11746024338461386681995936669409275054931640625, 0, 0, 0, -19895113660064588580108197261066338165074766609, 0, 0, 82819271780713079979935382926851738144130203648, 0, 0, 0, 0, 0, 0, 0, 0, -36495918309511014875960681030092422246046134119, 0, 55119516104912222740138590766766710716654464061, 0, 0, 0, 133407094578223470291786315517464136657499256052, 0, 74513682451168514736966550683252498023027002854, 0, 0, 0, 52637728326954960873480663352825518459018261721, 0, 0, -63061426240370676230762299437150141703975337984, 0, 0, 115802090236244568752994571209854087650944189914, 0, 0, 0, 0, 0, 0, 0, 83825919171099879295206391546849125506027769762, 0, 0, 0, 61557872207392374965856735328540154479438691221, 0, 0, 0, 0, -84563357566790276763032290197830086290913099776, -150798338026330452944677341298612232848053395831, 0, -173216443479559077317708801317056016500328097043, 0, 0, 0, 0, 0, 0, 0, 0, 38595486282742681625307768027717836433027760128, -412908906731529442412921873177975572907711969806, 0, 0, -253707463909116512315781323559587916357589532672, 0, 0, 0, 0, -156421258513585841688806080103686373459171920122, 0, 0, 0, 251520752952486009896242668853090277362684958398, 0, -734557971038533229795807326318846311327800362794, 283769853599440045170375559166366126455027400704, 0, 0, 371189731948005762885930857245134903759016121653, 0, 0, 0, 0, 0, 393635665961389552298426797551769842524034907366, 0, 0, 0, 0, 0, -543079515214953576100060283702869893822601598603, 0, 0, 0, 0, 505303290757859505136861272532170771626062774272, -338813178901720135627329000271856784820556640625, 0, 0, 193353277516610782847446867903662195575212736512, 0, 0, -243294574310588834532735215569796538753859144892, 0, -467810626113936680767013756004712004958058648818, 0, 0, 0, -670897942157163825456309496821221145595271962007, 0, 0, 0, 0, 0, 9787590586041074108267230470823958913110638006, 0, 0, 0, 0, 0, 0, 0, -395512491834888045734842889700733364389856434371, 445276959829618593024608413963638932403644268544, 0, 0, 0, 0, 669524434969350716985080602042650728933561317134, 0, 0, 0, 877442203511999455867727510458191721572202119601, 0, 0, 0, 0, 0, 0, 0, 1907756195370532139685362882246691400395072947574, 0, 0, 0, 1365661551977577934615700113263738965887720083406, 0, 1253614879140838611819052021019160747528076171875, 530711975185035777357896590052326307621901434880, 0, 0, -950923343432397762018097004308609673189805587306, 0, 0, 0, 0, 3017986637715605660176671921553162166737991368704, 0, 0, -551570924136413394914047755906802820809798914426, 2578131187173841733533256222549574963009962377216, 0, 0, -3730536720771485979582856649169519655819198785899, 0, 0, 0, 0, 0, 0, 0, 0, 1562605752378110000000000000000000000000000000000, 0, 0, 9054580589017766593927279701019663180817810218763, 0, 0, 0, 0, 0, -1941182676584292417014741854947020529178712326106, 0, -5617853116375173791286422439780356893277457450459, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4277414429884590554852086235591066202730247904287, 0, 7905415954962730361562186251304858701766908475942, -7332700022747944080558818989590111828789426126848, 0, 0, -8616036007198863804941914337262978923435450697386, 0, 9276795373176203958656300335781182908637935396018, 0, 0, -9912759030118240993087963732258753116772994383872, -3054305252388144657851987932874989309081029066623, 0, 0, 0, 0, 0, -2411118430490276388448246048822685171093234600531, 0, -18033798838893797099531389341502515170827034467038, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13779813011511736030919183704477717625040414821339, 0, 0, 0, 0, -11151591357276307911194412268594948138468393353216, 18307767380957952367575206197223303767921173552244, 0, 0, 0, 0, 0, -15654206349713840612161354989595332169015555163618, 0, 0, 0, 0, 11249694804530125128865213781452686900645454675968, -29733667795397721877962906906007047986020540147394, 0, 0, 23043457359555560777153261090683843038635332993024, 0, 0, -11408527753099510482457202742807567119598388671875, 0, 50803265036963600308771642548830519528216244810993, 0, 0, 0, 0, 0, 0, -5134463129262007413264206259792394067079860322304, 0, 0, 17224686450062951309529550165276785623318665766758, 0, 0, 0, 0, 0, -29616549664860692281301062601842243518523539167542, 0, 0, 20809147955466426404992396465576375741386846109696, 0, 0, 0, 0, 0, 0, 0, 97720256482148481654998227761463952174294123937792, 0, 0, 0, 0, 0, 0, 113496780016103475288441523521230043393748087978708, 0, -118455293460755516184861096546237502153455252853932, 0, 0, 0, -92011075447460564980236856816846945604084277593089, 0, -17274010319805379319140353985919083811986154318283, 0, 0, 0, 46891359932953318248024413149115769282464806558942, 0, 0, 0, 0, 0, -44457496807895072015311728709776430871246366708351, 0, 85436194857293896861617196792558044846159263514381, -67221879172204099805126099139726703675324441296896, 0, 0, 0, 0, 42211758665164886743129925480207044120070739514809, 0, 0, 0, 105332386545452845202913416449503733383410557391762, 0, 0, 62234127422640518541365517019592477460120651956224, 0, 0, 39920935886025232866856125390562709981402353274651, 0, -82334878902195232405179485342314829793895079324751, 0, 0, 0, 265161812300934142578061152849285132217681093659598, 0, 0, 0, 0, 0, 107974290683525000255199057434185504273965846716662, 0, 0, 0, 0, 0, 0, 0, -176748058825200964556823058779054674076768152989254, 52616108827129517817086927448365851211461902204928, 0, 0, -145980388536285935249583019612590982828737915377581, 0, -34652247988482789594667561448909321345657602341138, 0, 0, -89068667260896676793108055956137384708743377190912, -77411184181263951814769740056533448705102379220522, 0, 0, 0, 0, 0, -443944522647764085493975933761512698448371679956394, 0, 0, 0, 0, 0, -476622391439767033496946432294312359102295729292511, 0, 0, -253794025886673912346402638786876506231489882488832, 0, 0, 0, 0, 0, 0, 0, -166771816996665690000000000000000000000000000000000, 0, 0, 339984909446205876796010257138305891414781852053006, 0, 0, 0, -312354307628461747096825237433428855491177029056787, 0, 0, 0, 0, -401491018986975460431819200512928236942806768156672, 0, 0, 0, 73376989018989934955933665426824927866898683527168, 0, 0, 402892203587638240310027052551590127591006657092597, 0, -54389340431738503897461513962669017634209580966007, 0, 0, 0, 1000699498203364171504278535721823573112487792968750, 0, 456514495376692652529753928468348593437951756140173, 0, 0, 0, 183244156355987461875196541441573811777504927481366, 0, 0, 0, 0, 0, 354535778661321976499568399941957326258070715683182, 0, -403768536595670412063954785606354419082590733522634, 0, 0, 0, 0, 0, 0, 0, 0, 747358369326606889907410575211900956941949717184512, 133056124914388875805258045886572540157213402926991, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 124359470068527152257642002857360300254021340742312, 0, 0, -1051679112030903532366637803287121619940649736339456, 0, 0, 2093225320624451365380088765445092318614949931459974, 0, 0, 0, 0, -1234117467839216267610086446817757205550192419405824, -1679889407309076008022441908607926048038329694776503, 0, -498267514198001472069998348015360534191131591796875, 1318721452983965153531960968061824262875619258269696, 0, 0, 0, 0, -1732410100262136709157368422860393861871771950402802, 0, 0, 0, 0, 0, 0, 2399085596188743585827655309594003785187911410909184, 0, 0, -1700817868791981706259381955240815160599344186795787, 0, 2109268777036215833815195298385568596229423159478526, 0, 0, 0, 656775156586302344341174779248702526055687202774833, 0, 1851303105391304536074996137867794339795473629278389, 0], "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, -3], [1, 1, 7, 3, 1, 3, 0], [1, 1, 21, 8, -1, 6, 0]], "char_orbit_index": 8, "prim_orbit_index": 8, "minimal_twist": "21.35.h.a", "char_is_minimal": true, "conrey_index": 2, "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], [1, 0], [0, 0], [0, 129140163], [0, -17179869184], [0, 0], [0, 0], [-253015451951165, 48377438356677], [0, 0], [-16677181699666569, 16677181699666569], [0, 0], [0, 0], [2218611106740436992, -2218611106740436992], [-6628589056805300737, 0], [0, 0], [0, 0], [-295147905179352825856, 295147905179352825856], [0, 0], [0, 0], [10533550932831642194149, -10533550932831642194149], [0, 0], [-6247470274903719918351, -26426986431588396221544], [0, 0], [0, 0], [0, 0], [0, -582076609134674072265625], [0, 0], [-2153693963075557766310747, 0], [831118062424734792941568, 3515654303626917463457792], [0, 0], [0, 0], [0, -19599701438028304062305147], [0, 0], [0, 0], [0, 0], [0, 0], [286511799958070431838109696, 0], [-859594323581411974757802287, 859594323581411974757802287], [0, 0], [0, -856017071255852796440200131], [0, 0], [0, 0], [0, 0], [-8735048231520349599708750061, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-38115448583970168165554454528, 0], [61676442384098201771274374896, -22140102318154429307440875081], [0, 0], [0, 0], [0, 113878292870409011619438788608], [0, 0], [0, 0], [0, 0], [0, 0], [1360304484434680324510079506287, 0], [0, 0], [0, 0], [0, 0], [4468002075713925041487910419766, -4468002075713925041487910419766], [0, 0], [3412785335374113836958776271672, -4219584665012835036520971102885], [5070602400912917605986812821504, 0], [0, 0], [0, 0], [0, 22022844874719432605769728964013], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -20073068910160542409412259436943], [0, 0], [75169468182139098644256591796875, -75169468182139098644256591796875], [-180965027069048783591374550204416, 0], [0, 0], [0, 0], [-336858662185559380928110634527811, 336858662185559380928110634527811], [0, 0], [0, -278128389443693511257285776231761], [0, 0], [0, 0], [-454012169822031612418485802500096, 561342891875806038810731143495680], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [1677135456006139695378901262508605, -320674158487342173489716056970949], [0, 0], [2531108638458309585219648839318961, -2531108638458309585219648839318961], [0, 0], [0, 0], [0, 0], [2077823976048399144132689711232002, 0], [0, 0], [0, 0], [-10000000000000000000000000000000000, 10000000000000000000000000000000000]]}