Properties

Label 1.42.a
Level 1
Weight 42
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 1
Sturm bound 3
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 42 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{42}(\Gamma_0(1))\).

Total New Old
Modular forms 4 4 0
Cusp forms 3 3 0
Eisenstein series 1 1 0

Trace form

\(3q \) \(\mathstrut -\mathstrut 344688q^{2} \) \(\mathstrut -\mathstrut 10820953044q^{3} \) \(\mathstrut +\mathstrut 6271704903936q^{4} \) \(\mathstrut -\mathstrut 212302350281550q^{5} \) \(\mathstrut +\mathstrut 4970194114982976q^{6} \) \(\mathstrut +\mathstrut 57878416258239192q^{7} \) \(\mathstrut -\mathstrut 3555831711183237120q^{8} \) \(\mathstrut +\mathstrut 13277004110931878919q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut -\mathstrut 344688q^{2} \) \(\mathstrut -\mathstrut 10820953044q^{3} \) \(\mathstrut +\mathstrut 6271704903936q^{4} \) \(\mathstrut -\mathstrut 212302350281550q^{5} \) \(\mathstrut +\mathstrut 4970194114982976q^{6} \) \(\mathstrut +\mathstrut 57878416258239192q^{7} \) \(\mathstrut -\mathstrut 3555831711183237120q^{8} \) \(\mathstrut +\mathstrut 13277004110931878919q^{9} \) \(\mathstrut -\mathstrut 911610678410074173600q^{10} \) \(\mathstrut -\mathstrut 3064080929502798535164q^{11} \) \(\mathstrut -\mathstrut 71233189317945674062848q^{12} \) \(\mathstrut -\mathstrut 98515763053518962936694q^{13} \) \(\mathstrut -\mathstrut 663773359066872932212608q^{14} \) \(\mathstrut +\mathstrut 2322231962154213782968200q^{15} \) \(\mathstrut +\mathstrut 13217913642093764057038848q^{16} \) \(\mathstrut +\mathstrut 35582277130790298867301302q^{17} \) \(\mathstrut -\mathstrut 51949630971262524069430704q^{18} \) \(\mathstrut -\mathstrut 233456308095243376865478180q^{19} \) \(\mathstrut -\mathstrut 1234817679506740618000857600q^{20} \) \(\mathstrut -\mathstrut 784315067894306487816760224q^{21} \) \(\mathstrut +\mathstrut 10093688647003206881596695744q^{22} \) \(\mathstrut +\mathstrut 2812708670812770779627026056q^{23} \) \(\mathstrut +\mathstrut 36949405163940557660187279360q^{24} \) \(\mathstrut -\mathstrut 12630087813294771903109831875q^{25} \) \(\mathstrut -\mathstrut 445502868787427067716672131104q^{26} \) \(\mathstrut +\mathstrut 40981593702376529051426180280q^{27} \) \(\mathstrut +\mathstrut 526606706694181610802628184064q^{28} \) \(\mathstrut -\mathstrut 12736322664295346653179017670q^{29} \) \(\mathstrut +\mathstrut 6115742110948196616210957398400q^{30} \) \(\mathstrut -\mathstrut 55977552834365071134409017504q^{31} \) \(\mathstrut -\mathstrut 14842037794660482009412112744448q^{32} \) \(\mathstrut -\mathstrut 13829226714693448959900097020528q^{33} \) \(\mathstrut -\mathstrut 42547131667082319398961759011808q^{34} \) \(\mathstrut +\mathstrut 35330944415319146254058128592400q^{35} \) \(\mathstrut +\mathstrut 209583308279267044115700704156928q^{36} \) \(\mathstrut +\mathstrut 4945769903781582545269841455122q^{37} \) \(\mathstrut +\mathstrut 384288369224763756133358504473920q^{38} \) \(\mathstrut -\mathstrut 546470556552953849463965686898712q^{39} \) \(\mathstrut -\mathstrut 1326138456985596139721995183104000q^{40} \) \(\mathstrut -\mathstrut 3123151500646359746292805811918274q^{41} \) \(\mathstrut +\mathstrut 5023322329604694017661024056308224q^{42} \) \(\mathstrut +\mathstrut 1491980858362212236675453498061156q^{43} \) \(\mathstrut +\mathstrut 6827579920847638909574240093432832q^{44} \) \(\mathstrut -\mathstrut 3706804708974790460103758635956150q^{45} \) \(\mathstrut +\mathstrut 34089155258950859800971794327519616q^{46} \) \(\mathstrut -\mathstrut 63038106682044077762675687404413168q^{47} \) \(\mathstrut -\mathstrut 48906179099557375982971001333612544q^{48} \) \(\mathstrut -\mathstrut 97136113131667199274890334287198229q^{49} \) \(\mathstrut +\mathstrut 286202165340727366859498513545830000q^{50} \) \(\mathstrut -\mathstrut 157319866621422817701623275797858024q^{51} \) \(\mathstrut +\mathstrut 364999309722184195149034320029732352q^{52} \) \(\mathstrut +\mathstrut 79896749344137562310547533743021506q^{53} \) \(\mathstrut +\mathstrut 279506543662409583024224141017979520q^{54} \) \(\mathstrut -\mathstrut 1107430856215374719020572615529578600q^{55} \) \(\mathstrut -\mathstrut 1507500925934438536531619079138017280q^{56} \) \(\mathstrut -\mathstrut 120534128028213908789981458568129040q^{57} \) \(\mathstrut +\mathstrut 1060511497310363735425511566792954080q^{58} \) \(\mathstrut +\mathstrut 192512048683375799719343226678403860q^{59} \) \(\mathstrut +\mathstrut 5905677886285900358494072637173094400q^{60} \) \(\mathstrut +\mathstrut 8740556115036354715092732710435455386q^{61} \) \(\mathstrut -\mathstrut 12005332293025961804297174175449366016q^{62} \) \(\mathstrut +\mathstrut 4195060549596204507618981258341049336q^{63} \) \(\mathstrut -\mathstrut 28669651485797320669854651690478731264q^{64} \) \(\mathstrut +\mathstrut 23272939413910136331858458170260680700q^{65} \) \(\mathstrut -\mathstrut 70374114793184440562716940658640274688q^{66} \) \(\mathstrut +\mathstrut 11266872945514675454702655007279407852q^{67} \) \(\mathstrut +\mathstrut 95413181576279049358373233907724317184q^{68} \) \(\mathstrut +\mathstrut 110718129232411678126981084073658946848q^{69} \) \(\mathstrut +\mathstrut 59324379124057015483688060122385068800q^{70} \) \(\mathstrut -\mathstrut 140970915469820223119231433051520161384q^{71} \) \(\mathstrut -\mathstrut 178095780793081630529589944776993320960q^{72} \) \(\mathstrut +\mathstrut 45825493210252135256288871746499029406q^{73} \) \(\mathstrut -\mathstrut 255935787825178849200244145003411599008q^{74} \) \(\mathstrut -\mathstrut 247029389196459510298088488221820147500q^{75} \) \(\mathstrut +\mathstrut 26100578647791289060370838422069130240q^{76} \) \(\mathstrut -\mathstrut 429017620126390531124795910645506217696q^{77} \) \(\mathstrut +\mathstrut 3378623821652934155171000156043557135232q^{78} \) \(\mathstrut -\mathstrut 520184835554750143118446358634240850320q^{79} \) \(\mathstrut +\mathstrut 715918562852781559130521454428746547200q^{80} \) \(\mathstrut -\mathstrut 3191652631710460747876906046824191542997q^{81} \) \(\mathstrut -\mathstrut 579816777788457983576303882284492608096q^{82} \) \(\mathstrut -\mathstrut 619777491338381742927488037142663372644q^{83} \) \(\mathstrut -\mathstrut 4198672691855986319203859063793898610688q^{84} \) \(\mathstrut -\mathstrut 106299433069331216483654652405294143100q^{85} \) \(\mathstrut -\mathstrut 4751113477095326918262488958359640807744q^{86} \) \(\mathstrut +\mathstrut 13958176049210326842816445061163645008040q^{87} \) \(\mathstrut +\mathstrut 18329036816788093472347699011602935234560q^{88} \) \(\mathstrut -\mathstrut 142389067128374093799211866144944441010q^{89} \) \(\mathstrut -\mathstrut 8753545150081132110036071066039970208800q^{90} \) \(\mathstrut +\mathstrut 25080596935320871627133801126628392473296q^{91} \) \(\mathstrut -\mathstrut 67617289414955565381239604024555789723648q^{92} \) \(\mathstrut +\mathstrut 3477058704647981071307340824432458334592q^{93} \) \(\mathstrut -\mathstrut 53008068396962431152763933809330449227008q^{94} \) \(\mathstrut -\mathstrut 33170437179755379504247502944935502503000q^{95} \) \(\mathstrut +\mathstrut 95174464657114272630879818889875681181696q^{96} \) \(\mathstrut +\mathstrut 116011691364103339137369463947331771078182q^{97} \) \(\mathstrut -\mathstrut 38494567059701712876195969460820421029616q^{98} \) \(\mathstrut +\mathstrut 45849669342635847189814810549498192693428q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{42}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.42.a.a \(3\) \(10.647\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-344688\) \(-10820953044\) \(-2\!\cdots\!50\) \(57\!\cdots\!92\) \(+\) \(q+(-114896+\beta _{1})q^{2}+(-3606984348+\cdots)q^{3}+\cdots\)