Properties

Label 1.98
Level 1
Weight 98
Dimension 7
Nonzero newspaces 1
Newforms 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 98 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{98}(\Gamma_1(1))\).

Total New Old
Modular forms 8 8 0
Cusp forms 7 7 0
Eisenstein series 1 1 0

Trace form

\(7q \) \(\mathstrut -\mathstrut 16697241085008q^{2} \) \(\mathstrut +\mathstrut 100515854497394358147996q^{3} \) \(\mathstrut +\mathstrut 163057083940695061811962902784q^{4} \) \(\mathstrut -\mathstrut 3658387999529088680958306590731350q^{5} \) \(\mathstrut -\mathstrut 30592714388364079315260992082788233536q^{6} \) \(\mathstrut -\mathstrut 184642311743115370607493500489904481438408q^{7} \) \(\mathstrut +\mathstrut 36028528195426625427479134330455698506199040q^{8} \) \(\mathstrut +\mathstrut 34775775472129528349857305774273773877811641051q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(7q \) \(\mathstrut -\mathstrut 16697241085008q^{2} \) \(\mathstrut +\mathstrut 100515854497394358147996q^{3} \) \(\mathstrut +\mathstrut 163057083940695061811962902784q^{4} \) \(\mathstrut -\mathstrut 3658387999529088680958306590731350q^{5} \) \(\mathstrut -\mathstrut 30592714388364079315260992082788233536q^{6} \) \(\mathstrut -\mathstrut 184642311743115370607493500489904481438408q^{7} \) \(\mathstrut +\mathstrut 36028528195426625427479134330455698506199040q^{8} \) \(\mathstrut +\mathstrut 34775775472129528349857305774273773877811641051q^{9} \) \(\mathstrut +\mathstrut 2369114123959441270700616822719459966510786272800q^{10} \) \(\mathstrut -\mathstrut 211379321299339211995860033669883746379479318698796q^{11} \) \(\mathstrut +\mathstrut 29500590587146562092031430274877546417191966208812032q^{12} \) \(\mathstrut -\mathstrut 883667637845783834437332163606692334928033653755299614q^{13} \) \(\mathstrut +\mathstrut 24884922778173528138085777326574033504771595080747613568q^{14} \) \(\mathstrut -\mathstrut 1421739776861319561135033238174867421082029896683725376600q^{15} \) \(\mathstrut -\mathstrut 31468671341370205538262999960370611414173356196203424841728q^{16} \) \(\mathstrut +\mathstrut 163250436637003263661570089512096377905088225334685131721342q^{17} \) \(\mathstrut -\mathstrut 7054606772048003028382413409749231596837718873737440667537424q^{18} \) \(\mathstrut +\mathstrut 133084372359310898958448501523235681541051727436663191570359820q^{19} \) \(\mathstrut -\mathstrut 1318696260534044061297364386263469065025874939722479973417331200q^{20} \) \(\mathstrut -\mathstrut 8226961344750528298533572507576209983448935264598913374247505696q^{21} \) \(\mathstrut -\mathstrut 193421584410477868290586506488587370358898549812529751083484246976q^{22} \) \(\mathstrut +\mathstrut 925260914184001305416523826357059292226482310773339215111132964776q^{23} \) \(\mathstrut +\mathstrut 1719359518493251306391725804700467921422689016189510541760687554560q^{24} \) \(\mathstrut -\mathstrut 15111829774373494694703308579556617230149980669179989285410298974375q^{25} \) \(\mathstrut +\mathstrut 252570839996871764139482603418038366978372757286009959646749464447904q^{26} \) \(\mathstrut -\mathstrut 16291464003153760806194022590188439733978909915063668620863256233960q^{27} \) \(\mathstrut +\mathstrut 2270023864280230580582797832096861251181573169347509612847861972977664q^{28} \) \(\mathstrut -\mathstrut 119228645746988213289933973286594685848645193803889692652451844737975470q^{29} \) \(\mathstrut +\mathstrut 350448354156350400480979435069989695492221249186335731168327070817564800q^{30} \) \(\mathstrut +\mathstrut 1783283666881858864849681148885200501497581294973934227348751364131906784q^{31} \) \(\mathstrut -\mathstrut 5665372498136527985720301619489703024215195383428523596691479514791804928q^{32} \) \(\mathstrut +\mathstrut 31524650657546522511070078635079454480923539002999356172307109465073458512q^{33} \) \(\mathstrut -\mathstrut 360491523041063125717708388027762293189396999595568175085448186659598970272q^{34} \) \(\mathstrut +\mathstrut 1278268341035082746531666145800358760269267683649420892787253371588938750800q^{35} \) \(\mathstrut -\mathstrut 216561481226385812264597126278375191173372906326221899147967914271513631488q^{36} \) \(\mathstrut -\mathstrut 4532061622841943284542390241171859851726205146853788500539269747469617514358q^{37} \) \(\mathstrut -\mathstrut 2979582210919721773595405461863152858097797783237497905501709239616681227840q^{38} \) \(\mathstrut +\mathstrut 43268347489134056222423767530379619668087154910038087692852374564634305176712q^{39} \) \(\mathstrut -\mathstrut 252514831298472678734291758335102132215188475493571956673272319739362987008000q^{40} \) \(\mathstrut +\mathstrut 123663386655433999860484853403953500874113711440208020678841289201379470695974q^{41} \) \(\mathstrut +\mathstrut 3296122851141924824443574220618174749418258893075867148421980920155200276985344q^{42} \) \(\mathstrut -\mathstrut 6595249409358954185694714287710218939626711013706300289026511229489118746183244q^{43} \) \(\mathstrut +\mathstrut 31427981619155317050453798326367420934595218826815326227502736274099059309390848q^{44} \) \(\mathstrut -\mathstrut 252057107931731391251960224707597558538839631727412739243273361199825466582835550q^{45} \) \(\mathstrut +\mathstrut 333743461536679365083903174537100831945624746347277312419032904840551699600111744q^{46} \) \(\mathstrut +\mathstrut 1582413179705462665936960636748613012540566075462612818643843634715630112826042192q^{47} \) \(\mathstrut -\mathstrut 5861556434117332280930374286873664455351210291383528056190272983552191849213722624q^{48} \) \(\mathstrut +\mathstrut 4345635008055985505106601346877321132027699788278385269907095782368403364891488399q^{49} \) \(\mathstrut -\mathstrut 26742593205970009143775889336520990050133941492259748319418427757724876722706030000q^{50} \) \(\mathstrut +\mathstrut 7043565089506559965061572069632281800522096763383079376468682406398600422146676984q^{51} \) \(\mathstrut +\mathstrut 45800222007571685487736059984048709986270205428489770979037497696929384027946163712q^{52} \) \(\mathstrut -\mathstrut 653999931744204429821742741003701830521617657540517458768483866216741544701292475654q^{53} \) \(\mathstrut -\mathstrut 1692275654206728716605786947196644220317392594111136065941704729626944069981837438080q^{54} \) \(\mathstrut -\mathstrut 2797264930804680667438884831689324464716285797264284803651188210713133784740241832200q^{55} \) \(\mathstrut -\mathstrut 13571511538900847480549793700693331801076437559096966169392506220987757777557857402880q^{56} \) \(\mathstrut -\mathstrut 32156245276763940566100505959698139630384956043693169857398532690693294678041975751120q^{57} \) \(\mathstrut -\mathstrut 110275012470967940484400158535846043036245771061355495516009955997986614502808104491360q^{58} \) \(\mathstrut -\mathstrut 289716843512018767811919727809674339112407721830489506743846640027004030301179845118940q^{59} \) \(\mathstrut -\mathstrut 910863091257112962110410128770927709732237428874631129572443550789630933691032398899200q^{60} \) \(\mathstrut -\mathstrut 1779644273771380099149369471014727845406783738447834645166296866716596067825339549188046q^{61} \) \(\mathstrut -\mathstrut 4893410323209515393605311670149478112622973098189152140516775294151722525768562137565696q^{62} \) \(\mathstrut -\mathstrut 12773855755538157144284595252262546905649007916763284311597736303148976241726684562602024q^{63} \) \(\mathstrut -\mathstrut 24329532034212074257236420324752039539459926287390018025638252399891746834835822530789376q^{64} \) \(\mathstrut -\mathstrut 40979880706222898178317998710539228015340375450212825952623031288613904725454054500850100q^{65} \) \(\mathstrut -\mathstrut 142841613731497146561089386918878946227924637814625892149907766833242924230825872606056192q^{66} \) \(\mathstrut -\mathstrut 183094181851902905703789039636502649221241410347877100016575616698548103898875205122783908q^{67} \) \(\mathstrut -\mathstrut 250132580738896836682574414547500843555901286243235420681429272583107380144497499057716736q^{68} \) \(\mathstrut -\mathstrut 372244836961332226973480986215431578494847115740354696097669790201492502675456308855459168q^{69} \) \(\mathstrut -\mathstrut 587389541033882485666068522391834191601610745639266949076956170254929472707526921059782400q^{70} \) \(\mathstrut -\mathstrut 36618527208607574135274147674246343687098099724640001025727994874106062220116534447931656q^{71} \) \(\mathstrut +\mathstrut 2495502705800463241319297965149724088435827677064467496346161624547668625438549984339128320q^{72} \) \(\mathstrut +\mathstrut 5937141741627411574629383951784847225959103237898806939243808260531064318159784943464907526q^{73} \) \(\mathstrut +\mathstrut 25603418812897773069861990064614106209712057876935905208225093500026599325689360114519970848q^{74} \) \(\mathstrut +\mathstrut 43416229043729585532262686371625117245611844558141193068941674421259839404159894884059222500q^{75} \) \(\mathstrut +\mathstrut 64491781461168277038374423376126180174707623388661413952117963143585395013082375272839869440q^{76} \) \(\mathstrut +\mathstrut 122801524700573133455664123216977109508839271312008866744292206338517188364407357732160152224q^{77} \) \(\mathstrut +\mathstrut 256518622739178273010532892375526005382856863147760611859324715551823107217212845963281985152q^{78} \) \(\mathstrut +\mathstrut 155279975164311735091235448536513906273532801204307686975280157544842456609207922540776901680q^{79} \) \(\mathstrut +\mathstrut 343037548751841740038666995050634479050946344382038763901789904170114217394648666813900390400q^{80} \) \(\mathstrut -\mathstrut 799336653019442009471583631583081099983526554777301855450568718504605547656753900698628831153q^{81} \) \(\mathstrut -\mathstrut 2054599455199243418451530458808296516745297582440826399667363552358055209069956455679452833056q^{82} \) \(\mathstrut -\mathstrut 2745080838526935126539434486643898932954125805020264508203796620734019354440308801326974021684q^{83} \) \(\mathstrut -\mathstrut 12055830667015300843296227009204563031159870111997209215974794552386444770918151507927520305152q^{84} \) \(\mathstrut -\mathstrut 16156906986132970771716277890961343081101351325821342812927748903601690598916612215092853170700q^{85} \) \(\mathstrut -\mathstrut 16073101085057033129856695763368798351047883803740227513388827997968391823543719379002604387776q^{86} \) \(\mathstrut -\mathstrut 44931373084677669249994770736329381356923858000626008622029156778901658182110994195783000791480q^{87} \) \(\mathstrut -\mathstrut 20900444501134905678673788524771632932447417317035512416151379720801969394444956958395302789120q^{88} \) \(\mathstrut +\mathstrut 8652425236627243255051028260917634407304730072980172181544783646255542601500269383337979350390q^{89} \) \(\mathstrut +\mathstrut 169914380219009102880054256907856294069041898142575788262717672760376053145875718225670932330400q^{90} \) \(\mathstrut +\mathstrut 235279610532724372901602846332263408075886672274330172793822218199845308058643167074949650230544q^{91} \) \(\mathstrut +\mathstrut 622950794384614085632156625042963081233986358617743991991586248417198315809579918444522808891392q^{92} \) \(\mathstrut +\mathstrut 1619655729334717431421579797164299646702152339363664709672746834797775058100318492643375449441152q^{93} \) \(\mathstrut +\mathstrut 1784387548746436753701888750274366538460858609156963702431495773056050960861585984793528939671808q^{94} \) \(\mathstrut +\mathstrut 1109691419127482658877926123378178695834970817464791602098716148821958373905367930889408748989000q^{95} \) \(\mathstrut +\mathstrut 2773817117979873680694700349927475687549477810523157816910439588411515192104026991177258420404224q^{96} \) \(\mathstrut -\mathstrut 462826972284038426621245345324758076530452205891330025493894671876723283114629445572915788984658q^{97} \) \(\mathstrut -\mathstrut 10100804559243313775965110405631054964918520327952856127425837778067309219959758215138751854831056q^{98} \) \(\mathstrut -\mathstrut 13792894935722775136702660269810636953813664741795563019740674282913700184659028566406972539495228q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{98}^{\mathrm{new}}(\Gamma_1(1))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1.98.a \(\chi_{1}(1, \cdot)\) 1.98.a.a 7 1