Properties

Label 1.102.a
Level 1
Weight 102
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 8
Newforms 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 102 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{102}(\Gamma_0(1))\).

Total New Old
Modular forms 9 9 0
Cusp forms 8 8 0
Eisenstein series 1 1 0

Trace form

\(8q \) \(\mathstrut -\mathstrut 434989091795040q^{2} \) \(\mathstrut -\mathstrut 1209375896611771518910560q^{3} \) \(\mathstrut +\mathstrut 9008967123164113911511576503296q^{4} \) \(\mathstrut +\mathstrut 38238791540232828026421308589217200q^{5} \) \(\mathstrut +\mathstrut 2477260046146272006672820535971480695936q^{6} \) \(\mathstrut -\mathstrut 5786789720778120168956257648884421874283200q^{7} \) \(\mathstrut -\mathstrut 6101688461407407841888405145259998920458731520q^{8} \) \(\mathstrut +\mathstrut 5273640617280587177839635242070674204864681879784q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut -\mathstrut 434989091795040q^{2} \) \(\mathstrut -\mathstrut 1209375896611771518910560q^{3} \) \(\mathstrut +\mathstrut 9008967123164113911511576503296q^{4} \) \(\mathstrut +\mathstrut 38238791540232828026421308589217200q^{5} \) \(\mathstrut +\mathstrut 2477260046146272006672820535971480695936q^{6} \) \(\mathstrut -\mathstrut 5786789720778120168956257648884421874283200q^{7} \) \(\mathstrut -\mathstrut 6101688461407407841888405145259998920458731520q^{8} \) \(\mathstrut +\mathstrut 5273640617280587177839635242070674204864681879784q^{9} \) \(\mathstrut -\mathstrut 376167658847177398692429835067300112512860198593600q^{10} \) \(\mathstrut +\mathstrut 4622006661480385115355021397632645270205791478300896q^{11} \) \(\mathstrut -\mathstrut 7273290781506553143908216801865849714958844187989422080q^{12} \) \(\mathstrut +\mathstrut 250316830865150221699601352256397536965043294984328650480q^{13} \) \(\mathstrut -\mathstrut 4856789037716039923353321450215036970203737520869624889088q^{14} \) \(\mathstrut -\mathstrut 296460708185002952419818874947342543917521978696100167156800q^{15} \) \(\mathstrut -\mathstrut 10662656154906175558835021484824464714661655552497093859868672q^{16} \) \(\mathstrut -\mathstrut 397968518694853312322660892941326449007299986932512193696587120q^{17} \) \(\mathstrut -\mathstrut 7270968925217398747066352706388703938040714138623386028515252960q^{18} \) \(\mathstrut -\mathstrut 21387776045417165942123954421061470474744368808488511816400717280q^{19} \) \(\mathstrut +\mathstrut 1745002690168409059221421019241581897927614179506161156200285542400q^{20} \) \(\mathstrut +\mathstrut 4030935126807879780648600654579655736182360851489572706466859540736q^{21} \) \(\mathstrut +\mathstrut 61357881995862711169740037407631980426480577127973320405539739944320q^{22} \) \(\mathstrut -\mathstrut 1366243345208606848425464574347748611753917469593153677393324561698880q^{23} \) \(\mathstrut +\mathstrut 10457354719000260635321058863018299052737315743164922361342586480885760q^{24} \) \(\mathstrut +\mathstrut 77471873089568593564333770877949420045843582630742632687744142562715000q^{25} \) \(\mathstrut -\mathstrut 97549630676937426518340388130407212490384846814009484188479115327886144q^{26} \) \(\mathstrut -\mathstrut 5951874968930013487417142282111771144801435961988629201748805497863184320q^{27} \) \(\mathstrut +\mathstrut 9217624035174751886516129105576165061663773766415040330328487084880404480q^{28} \) \(\mathstrut +\mathstrut 15465799862710125255662370242568323665682807414567501281109138719156160880q^{29} \) \(\mathstrut +\mathstrut 1101689156065505631051293671607641382064945196508526428823375711603202118400q^{30} \) \(\mathstrut -\mathstrut 6594370386043135339784923725045360443937393326734068279132668478779615001344q^{31} \) \(\mathstrut +\mathstrut 12265519409733718324179959581296851912742484455832107241543734281342036213760q^{32} \) \(\mathstrut +\mathstrut 43813172582105581329585760338258562815639759809845990212191452867766348215680q^{33} \) \(\mathstrut +\mathstrut 9531455444774917507766540524882635666895777953789094347547215472626183995712q^{34} \) \(\mathstrut -\mathstrut 1122850631208004175280217132184898888977788452428069383882586628450512616297600q^{35} \) \(\mathstrut +\mathstrut 1966242586607976986737003826554029255087710066072863106322127653222050407339008q^{36} \) \(\mathstrut +\mathstrut 39729696767983511833540209209183332457877293383323859312175998401968644864715440q^{37} \) \(\mathstrut -\mathstrut 70873740526925065519455012686645778106113298999572267198467188879790467046148480q^{38} \) \(\mathstrut -\mathstrut 269289195198196884798470270521708844679404215685249767615656452740889673105306432q^{39} \) \(\mathstrut -\mathstrut 763642761360299050617237751714968411270996317577517686387843428508400019349504000q^{40} \) \(\mathstrut +\mathstrut 5607291724825101314952096252772109505395882457063737303656079003304969203257094736q^{41} \) \(\mathstrut +\mathstrut 3008066923831569706716293907931878334959183836053498604235677758281531565332526080q^{42} \) \(\mathstrut -\mathstrut 28642921955044714117801359306021921736063108483729021321044095944585527287681223200q^{43} \) \(\mathstrut -\mathstrut 207838425393205175674959052733026300855796348257745356716186803699782799277851086848q^{44} \) \(\mathstrut +\mathstrut 712633045382921242540931880134776511927082560144290402835715503414563529286220047600q^{45} \) \(\mathstrut +\mathstrut 1088094260619851586903932234100844276278561023621942541398958535856528393570339218176q^{46} \) \(\mathstrut -\mathstrut 4595399220200007631460417274797048154524720407021496316223236391731855709593438718080q^{47} \) \(\mathstrut -\mathstrut 58354182581817955899154335674671016574355963424701638945735582725996041826866298880q^{48} \) \(\mathstrut +\mathstrut 12068461406676719302337658501270392621238416595305390197216228129207599916872005856456q^{49} \) \(\mathstrut -\mathstrut 40493179837482260394665357435432250163405353367416857829233726008281167215503492420000q^{50} \) \(\mathstrut +\mathstrut 117646730044094759803745147399491979694134742922341911657750530682089815486256248611136q^{51} \) \(\mathstrut -\mathstrut 736020167800817028850658909331852777746165402605863935107936992324104798352324258252800q^{52} \) \(\mathstrut +\mathstrut 131026696145917691346168139299202731343660174597285772716290345361212508775951813313840q^{53} \) \(\mathstrut +\mathstrut 6803608957095266771149163140167539716357850176039815317805755392633822625226741503089920q^{54} \) \(\mathstrut -\mathstrut 14585157967675450217148723878599628333971210001615112897255333178063634767400530051473600q^{55} \) \(\mathstrut -\mathstrut 23665562342657326400415121984960944704012341384928617813498515591030351969339927087022080q^{56} \) \(\mathstrut -\mathstrut 66899487754306674554237314096607510056291565049587799982155034523058479948455991635655040q^{57} \) \(\mathstrut +\mathstrut 29173417521771002425120779628349939892591335515731485644911210555324770598093888308326080q^{58} \) \(\mathstrut +\mathstrut 212583149562022564923669670483574922097682552074321909615339251529169016840977455874187360q^{59} \) \(\mathstrut -\mathstrut 3455800135608334392541843481344001808338357411235959344412061781382196941870275476295065600q^{60} \) \(\mathstrut -\mathstrut 3390796423636162146406492296389682436951029380958058095674208836333532599894943317230895504q^{61} \) \(\mathstrut -\mathstrut 5878859817222970028213836429448832127296537243368792127423103234889716583457526212133370880q^{62} \) \(\mathstrut -\mathstrut 20171938924061808002384576493874339158887341995607670819297079343133751793255425885494984640q^{63} \) \(\mathstrut -\mathstrut 74870090698021647967203019932764377907062372989513317693678846896652408519412785858115272704q^{64} \) \(\mathstrut -\mathstrut 161067075283368767182138254547148962244907084326790507487294907612770451283405321317426536800q^{65} \) \(\mathstrut -\mathstrut 745278055170676259198413344675313071673593040227005461838089798951153726758412015071955911168q^{66} \) \(\mathstrut -\mathstrut 618774503558862942537948810466095132313460919373052732511642097824837019429997681150398682720q^{67} \) \(\mathstrut -\mathstrut 2182412150351293808121583165511486752102068977919329447376923905220322529537335456462676162560q^{68} \) \(\mathstrut -\mathstrut 5393950442083315109606578094475120918497802785657891521452512469623636760248087300551286537472q^{69} \) \(\mathstrut -\mathstrut 12923520657540473465038555822652190723092643731233782501675276653712048411292540691873715571200q^{70} \) \(\mathstrut -\mathstrut 15797470289857673806303846655911576507977904169297655042639265226995032204172380517793831135424q^{71} \) \(\mathstrut -\mathstrut 55126715113590704564504537983251285080485074916503283789364546398928839504287032847376708239360q^{72} \) \(\mathstrut -\mathstrut 20462651635605668591994589976366754984142669867347912050159975933828495442291952971923777071280q^{73} \) \(\mathstrut -\mathstrut 142953411935712165334538916257020870493984381200782662943456748743148514063783881306064429441088q^{74} \) \(\mathstrut -\mathstrut 204312291750914950304829914412770260373631281822544572731633720960361618548975517964814619460000q^{75} \) \(\mathstrut +\mathstrut 64556217054886497186737063238064337992823205997653378371004031509089422583081356800943896432640q^{76} \) \(\mathstrut +\mathstrut 250231448169383959900618348975396989794902211753647918986458150866408618577007907131029306438400q^{77} \) \(\mathstrut +\mathstrut 1260981709052401111398092363772739439414079820346824747462408082793911096042108256417770344646400q^{78} \) \(\mathstrut +\mathstrut 1474556321278768744579716979675929750918930811984805387023357390321899878561204701118206999166080q^{79} \) \(\mathstrut +\mathstrut 6033438037435277941170744030808192554572458649979375320464765273747209092446481051552234550067200q^{80} \) \(\mathstrut +\mathstrut 14613214105102112111129469132612601529386527627758931132459526147171392070559192290643105065182408q^{81} \) \(\mathstrut +\mathstrut 30083863369214129982421840097969977845328701273986110579467106900080547794123383776302929686086720q^{82} \) \(\mathstrut +\mathstrut 33762254529254022439253159341806143692643909652777369725086142424861011401680843403961249425712160q^{83} \) \(\mathstrut +\mathstrut 57799153837692447414380568170128797835929379783304235587752969314531310322308849537769529417695232q^{84} \) \(\mathstrut +\mathstrut 17314966267116570951109803841412092095679328201414316724042066880549149931729490643535478494114400q^{85} \) \(\mathstrut +\mathstrut 67989564188024628582959760637462873453376851598916319417912395832044408164663357850732592560556416q^{86} \) \(\mathstrut +\mathstrut 2586434133428712948881772736535019341274237946379240114707154003676967765014837223291966941531840q^{87} \) \(\mathstrut -\mathstrut 363099602372059077387783242048689913608334478213970275423791339756517232974574737922754584123146240q^{88} \) \(\mathstrut -\mathstrut 620007165949691950044675276484549383308720953973642955804615855186521697520022438525123333812557360q^{89} \) \(\mathstrut -\mathstrut 4716676146177962028099989697458384454375488041754925418224025761569034561814581975790426208019028800q^{90} \) \(\mathstrut -\mathstrut 3685711793015793225308940042728501386995879977832891226647110522985454537354035281338855172828873344q^{91} \) \(\mathstrut -\mathstrut 4618779932089713137770970202224414792688843158843334085630908366025929325979388063902511470793400320q^{92} \) \(\mathstrut -\mathstrut 3975022445092224432029728046757042348886229630318622378634497589784647142077875089398179428115102720q^{93} \) \(\mathstrut -\mathstrut 17371370943540992303713705925513939673302729250250795188383540356993592041601425149438637190677682688q^{94} \) \(\mathstrut -\mathstrut 2642077700832720169247174948884057845373174576960370774287679094739730873649398763127258995555528000q^{95} \) \(\mathstrut +\mathstrut 4679875418673156206717240026356824763600126819048403120235276936002238426687957733980747642601209856q^{96} \) \(\mathstrut +\mathstrut 64020476116668335744724892375903667651900818166631138467214326399663196857065619648203365824701173520q^{97} \) \(\mathstrut +\mathstrut 202971561788470754768820264959327860776947519106194867162872422213964707447467488105939520314595817120q^{98} \) \(\mathstrut +\mathstrut 225914901454627435116272921386700923755368861971179328902362103653753469396751969300619190223813523808q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{102}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.102.a.a \(8\) \(64.601\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\!\cdots\!40\) \(-1\!\cdots\!60\) \(38\!\cdots\!00\) \(-5\!\cdots\!00\) \(+\) \(q+(-54373636474380-\beta _{1})q^{2}+\cdots\)