Properties

Label 1.122.a
Level 1
Weight 122
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 9
Newforms 1
Sturm bound 10
Trace bound 0

Related objects

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 122 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{122}(\Gamma_0(1))\).

Total New Old
Modular forms 10 10 0
Cusp forms 9 9 0
Eisenstein series 1 1 0

Trace form

\(9q \) \(\mathstrut -\mathstrut 2345005562254519728q^{2} \) \(\mathstrut -\mathstrut 45298662406895255983997747004q^{3} \) \(\mathstrut +\mathstrut 8462901481545657250924227818768095488q^{4} \) \(\mathstrut -\mathstrut 1892628936004587162449482404208025942059050q^{5} \) \(\mathstrut -\mathstrut 169155345437237254853213475765636376857034060992q^{6} \) \(\mathstrut +\mathstrut 2195742607988216453868262401462060909846066161833992q^{7} \) \(\mathstrut -\mathstrut 6498505205013969366907252193209867920059782603760087040q^{8} \) \(\mathstrut +\mathstrut 7945503363883566160952357352391639075761121301070127960917q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut -\mathstrut 2345005562254519728q^{2} \) \(\mathstrut -\mathstrut 45298662406895255983997747004q^{3} \) \(\mathstrut +\mathstrut 8462901481545657250924227818768095488q^{4} \) \(\mathstrut -\mathstrut 1892628936004587162449482404208025942059050q^{5} \) \(\mathstrut -\mathstrut 169155345437237254853213475765636376857034060992q^{6} \) \(\mathstrut +\mathstrut 2195742607988216453868262401462060909846066161833992q^{7} \) \(\mathstrut -\mathstrut 6498505205013969366907252193209867920059782603760087040q^{8} \) \(\mathstrut +\mathstrut 7945503363883566160952357352391639075761121301070127960917q^{9} \) \(\mathstrut -\mathstrut 1722648625287605771733277740799503204814238573365164973293600q^{10} \) \(\mathstrut -\mathstrut 946247437041242628794010189459909585820203760454440287613552692q^{11} \) \(\mathstrut +\mathstrut 205846961050281878415699597946796712976603670706873231298938012672q^{12} \) \(\mathstrut +\mathstrut 20596127771705642483605985955370331334854065669132980339746788779486q^{13} \) \(\mathstrut -\mathstrut 6541972694294346334011779110963479954883365352702523229035305330483584q^{14} \) \(\mathstrut +\mathstrut 94761650294240619608372286408346994746207880434327141095820600145938200q^{15} \) \(\mathstrut +\mathstrut 15125444512952621416063439206177933863772762787209602627890080570611400704q^{16} \) \(\mathstrut +\mathstrut 291951493650412549850834598805724750617640895870041885121831690800331035682q^{17} \) \(\mathstrut -\mathstrut 2554000175718076948380008722939707666960273565314048023897922364658130426864q^{18} \) \(\mathstrut +\mathstrut 30244684445956612332670117612595525326891015746649482369862884848315284461780q^{19} \) \(\mathstrut +\mathstrut 4562951142663369182841621952582280345228980283169468426672463108421372089382400q^{20} \) \(\mathstrut +\mathstrut 35146001071237823021693437259813836720201207139254364736561723878685716530560288q^{21} \) \(\mathstrut -\mathstrut 1908843328157955617823816866863990801015534541375661383005747627202736697921398336q^{22} \) \(\mathstrut -\mathstrut 66547277273309692585260941575189421012052896396341670760157778423156238686357058024q^{23} \) \(\mathstrut -\mathstrut 752736756299124610400627977416074789098074869027579302337966622137134625951047925760q^{24} \) \(\mathstrut -\mathstrut 6063954929776831553687695824368630787209822932539681432479202799269060736255468175625q^{25} \) \(\mathstrut -\mathstrut 68842531925347949534946832128658250301897561117051749502543801676148842557574912147872q^{26} \) \(\mathstrut -\mathstrut 599094982712902977137778651999579486037062432725587105690436473582035154107389795716440q^{27} \) \(\mathstrut +\mathstrut 14581457392452701650088858542793969027985828891624009507886840217572255356341773965625344q^{28} \) \(\mathstrut +\mathstrut 9039340472411915035494616975186209221844392206687458522714064361334880069082093346905070q^{29} \) \(\mathstrut +\mathstrut 224260392412850366562482895689598093094206490242486949280006808962977358350861560270998400q^{30} \) \(\mathstrut -\mathstrut 1034214344782654758430975917538809236085530199413694042134266190861671432181122576926086112q^{31} \) \(\mathstrut -\mathstrut 32504525000929540761398714812123921617256100597234986820033520241386493923631009832383807488q^{32} \) \(\mathstrut +\mathstrut 189949463814086324300823839088808170132383689196162349649439549175970470599919775108948927152q^{33} \) \(\mathstrut +\mathstrut 939230388337351560267419962761669652735221862277825209065568487608538630630957599920217170336q^{34} \) \(\mathstrut +\mathstrut 1343144021786280211948320998755385153610555228046229864187689603416027546078320739943060612400q^{35} \) \(\mathstrut -\mathstrut 21747907752251375975427518389059436655823261956750397535228718126776457105689705407608776563456q^{36} \) \(\mathstrut -\mathstrut 88515341604947210488499310221844243003334043790663530401335727647981800120006279439706998268938q^{37} \) \(\mathstrut +\mathstrut 126431143256035943119117270678428356969446546517968603954366283120911078870917992997220500555840q^{38} \) \(\mathstrut +\mathstrut 217837571218652472832776380975246155068206021757529611026730729062256423563336349872452629634104q^{39} \) \(\mathstrut +\mathstrut 11699272454320878743488987607870545498317393987884112075950101149279048493373249852479799479296000q^{40} \) \(\mathstrut -\mathstrut 36266094262194860707738000735265088509116494488735889525314316314221341311667592777599187406913222q^{41} \) \(\mathstrut -\mathstrut 24787352510041822155108090768801766655788422577097156255869676682213614031202393800364112862967296q^{42} \) \(\mathstrut -\mathstrut 232370696794750496427815530982465444104722554898177200564202440384179721532324359363059913691265044q^{43} \) \(\mathstrut +\mathstrut 7755327422511594524608603055387018294701513657236683851986386901343418513803274064133364624004320256q^{44} \) \(\mathstrut +\mathstrut 3247131420778261129864754583862668667744851710389803065112927478198766013287651133195234793708696350q^{45} \) \(\mathstrut -\mathstrut 32066987947547067490416916557196164509339083485720964163476500441257367761070295505033101035894375552q^{46} \) \(\mathstrut -\mathstrut 132970274906173452814801214841116212222140439777467383504750807710754558312919347426848207706456695248q^{47} \) \(\mathstrut +\mathstrut 1792993240520940040285669530334719652675802655317197830920369780797223163120464508596735702234386661376q^{48} \) \(\mathstrut +\mathstrut 3971615803493637002463922107037659765667323348806045910695714957649057905572825978452768033947465237313q^{49} \) \(\mathstrut +\mathstrut 7697223557528977921454596784007095645216064886088735712319363716221302227247960859603436865144030830000q^{50} \) \(\mathstrut -\mathstrut 12851187227364644420645646585565612980157473692407810028414511867222315540665892049707079694243262493752q^{51} \) \(\mathstrut +\mathstrut 41491246868006007350968584983945986180424656334954442495103497331692372835472248671859508511281974820352q^{52} \) \(\mathstrut +\mathstrut 10921805138133777254090784536986505203689729704788186882887817145907729071674310284399320645165776125446q^{53} \) \(\mathstrut +\mathstrut 1339620561670595781535503143383501960027220441835890399944886982813214108542142442500405331111067486871680q^{54} \) \(\mathstrut -\mathstrut 1312854241531753321574015681587452449577731960880104498235108054018717321131599152359037095554839302748600q^{55} \) \(\mathstrut -\mathstrut 14013489107783484379024464711764338924776495535033134010566539603721944518516633929838564532681379280158720q^{56} \) \(\mathstrut -\mathstrut 31019370720452892632999266840260901115398140535819179494909299925851052488218537305068762474072132809464880q^{57} \) \(\mathstrut +\mathstrut 103566512036259767730142842802003772713045020405103287191675134464175461494809359502286741327442998854097760q^{58} \) \(\mathstrut -\mathstrut 212654227372156556243821221093344570156200984495183110384877226881440240904587127248726963633402442388397060q^{59} \) \(\mathstrut -\mathstrut 422775085570641982781661820780199899688061805673956240019260238835680896536027096304091002230119430523545600q^{60} \) \(\mathstrut +\mathstrut 1192163308009290988314718399559245385155131325092676542388200473202899841355909578157895873548972217626937358q^{61} \) \(\mathstrut +\mathstrut 1941577256261942079284748865266177577315768005250991995768914948259042107075822164327427075406958896697915904q^{62} \) \(\mathstrut +\mathstrut 451398588142208697776529182978564850520004037586377967283679997710918662905240621028803130635870486918043496q^{63} \) \(\mathstrut +\mathstrut 58844915592066748224918413663360071934978670807229624180238002804297923325840628846335879209980431060401389568q^{64} \) \(\mathstrut -\mathstrut 41307677239725606429137681882540847206257959638235776751518537901187469657040797622415542482923664688418764300q^{65} \) \(\mathstrut -\mathstrut 222086041679950312339781078110357023370750120852496118683208049646663973764702391499379128192551147975013941504q^{66} \) \(\mathstrut -\mathstrut 136956255883591433626896738276452320541908670428347212980145870863327851773988143589420054081089733226508975868q^{67} \) \(\mathstrut -\mathstrut 141094811799092295974464545753546540483126567546619661037683966526498908594653379053568196980211372687791832576q^{68} \) \(\mathstrut +\mathstrut 1325703171238765045361423824776857588261240408135555321965899246235283904667578177535332268855352594559670964064q^{69} \) \(\mathstrut +\mathstrut 251934589370384384494289262861906043864096277276788575857738394556055301564200175196895771626792095349002028800q^{70} \) \(\mathstrut -\mathstrut 21585422985838182545762327030440661631324036114582384867758341692032917773329287240302446531581657134820891213752q^{71} \) \(\mathstrut -\mathstrut 5181834258416339630015764026055527646506354416168007949107924953264135981412995982436721696529253639785101291520q^{72} \) \(\mathstrut +\mathstrut 91235460780032725960652165272631372912505283323159668796891496309162099636399114489032757775807008811684035374426q^{73} \) \(\mathstrut +\mathstrut 310562981122696891225427716699672479798427405954878722327169646078571868354993002411909262537623251852286369642976q^{74} \) \(\mathstrut +\mathstrut 43065854506087315183339457241248482679331791698024061594158993211332750535581795467446263657604087829943816477500q^{75} \) \(\mathstrut -\mathstrut 1628928259080846394930799553567522291541981414122456953774556713740025206052658836539555750192733076653498088483840q^{76} \) \(\mathstrut +\mathstrut 593398979324677723779464865172133117018002924612325496238799373091215617849415550444705675974821710181802828350304q^{77} \) \(\mathstrut -\mathstrut 6873235601534959334329744558974767766222222958184019979663697300957230011165665645661869140437348638585389730736768q^{78} \) \(\mathstrut +\mathstrut 12451904914912678516471799458709519750612136226261564829575149335945412565470277464754582893898189772426218896816720q^{79} \) \(\mathstrut -\mathstrut 20416950898306426146345946546741629794844904073553249082791509645594723097676639519064500446972597103490830240972800q^{80} \) \(\mathstrut -\mathstrut 40856231575215745746855879250733371261216334279125203008573307569275978049909264916389709598337529820618984078592511q^{81} \) \(\mathstrut +\mathstrut 32147344949534769988675834932358838024355394065520493232144096322964430678203949090265848270504974541383740855029024q^{82} \) \(\mathstrut -\mathstrut 92550876115215159531985566894207205907616571001151579100140340424113698287990359504129121116969620392280333900687084q^{83} \) \(\mathstrut +\mathstrut 149786622283872863814961679878718479671325736759801797089969582016734283953793144464030325178406284102124769637769216q^{84} \) \(\mathstrut -\mathstrut 457768087179221548903179340844196170221647881541175735561813412251720733334690809762523483946456540131705087221018100q^{85} \) \(\mathstrut -\mathstrut 2597491864434159334587628292949145911098969463321219405661773952780499099399232684938429948876042525744324616394370112q^{86} \) \(\mathstrut -\mathstrut 6860132173224607170538777320017488364980901889195600241683572931313063475309515779498812905462751134050092231747965320q^{87} \) \(\mathstrut -\mathstrut 20006125934411614149040201757441776841868885955363484760412796241321136345672966303804893860326010500704122960860692480q^{88} \) \(\mathstrut -\mathstrut 6037951059942933692255237205803554193360594969996068937834548367886153095083618336696729724512143193617265723073840790q^{89} \) \(\mathstrut -\mathstrut 63101356532716899775688972110257991639639781786779198684055149646555511091876460642986977143928184313177571126402448800q^{90} \) \(\mathstrut -\mathstrut 123641023753197596743476339553493022736411481279426005005225341366808933988856782685240985478245146307872825619974888592q^{91} \) \(\mathstrut -\mathstrut 364595199967728361741013600374859006514622011131757842452690960184887037990775378757973866446814260984048497269830739968q^{92} \) \(\mathstrut -\mathstrut 660210659270707805852573362768494443983824981820503945313596568722380303376948547337519220648409914639203450549706054528q^{93} \) \(\mathstrut -\mathstrut 1077366499492799036766200119308272598652452209354508770841202268675762751723923474906601231339334467643845894468443138304q^{94} \) \(\mathstrut -\mathstrut 1952811193153518003415269978917451688485843585663036733937657231131838392410846728976735534304153554615423725772929253000q^{95} \) \(\mathstrut -\mathstrut 7973910491229034017269638806130805343748566540122585079441423327960922891988630774830062893111316529474837792857136300032q^{96} \) \(\mathstrut -\mathstrut 10257092292553957046050140760321382189656293894451103156433186039799204062322028715705878067672306955149219750865890726798q^{97} \) \(\mathstrut -\mathstrut 27691496134014026270502117819887007317432773944983420293676841151578333911041338924275151210232199410900266664836266600496q^{98} \) \(\mathstrut -\mathstrut 44066255828766064795825662460182521807738019967004038392602001105306909448583819181101964434724044331056342593475150607396q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{122}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.122.a.a \(9\) \(92.717\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-2\!\cdots\!28\) \(-4\!\cdots\!04\) \(-1\!\cdots\!50\) \(21\!\cdots\!92\) \(+\) \(q+(-260556173583835525+\beta _{1}+\cdots)q^{2}+\cdots\)