Properties

Label 3.41.b
Level 3
Weight 41
Character orbit b
Rep. character \(\chi_{3}(2,\cdot)\)
Character field \(\Q\)
Dimension 12
Newforms 1
Sturm bound 13
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 41 \)
Character orbit: \([\chi]\) = 3.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(13\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{41}(3, [\chi])\).

Total New Old
Modular forms 14 14 0
Cusp forms 12 12 0
Eisenstein series 2 2 0

Trace form

\(12q \) \(\mathstrut -\mathstrut 372082572q^{3} \) \(\mathstrut -\mathstrut 4781373657072q^{4} \) \(\mathstrut +\mathstrut 8471862485327952q^{6} \) \(\mathstrut -\mathstrut 94341749124766584q^{7} \) \(\mathstrut -\mathstrut 23605502262041939220q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 372082572q^{3} \) \(\mathstrut -\mathstrut 4781373657072q^{4} \) \(\mathstrut +\mathstrut 8471862485327952q^{6} \) \(\mathstrut -\mathstrut 94341749124766584q^{7} \) \(\mathstrut -\mathstrut 23605502262041939220q^{9} \) \(\mathstrut -\mathstrut 129384136354706290080q^{10} \) \(\mathstrut -\mathstrut 4708039830028985428272q^{12} \) \(\mathstrut +\mathstrut 704368845864154901976q^{13} \) \(\mathstrut +\mathstrut 320935800901459838631840q^{15} \) \(\mathstrut +\mathstrut 6054431850962872672227456q^{16} \) \(\mathstrut +\mathstrut 10227710367381761273509920q^{18} \) \(\mathstrut +\mathstrut 37616619688417835612151720q^{19} \) \(\mathstrut -\mathstrut 179163719456723608834234728q^{21} \) \(\mathstrut +\mathstrut 846315150249292772829325920q^{22} \) \(\mathstrut -\mathstrut 18213480358094369517645250944q^{24} \) \(\mathstrut +\mathstrut 8842265325510151276196474700q^{25} \) \(\mathstrut -\mathstrut 70717074113738779393083858252q^{27} \) \(\mathstrut +\mathstrut 469404222007499612173589889696q^{28} \) \(\mathstrut -\mathstrut 207809636542026559976510503200q^{30} \) \(\mathstrut -\mathstrut 914600368399753689553849145016q^{31} \) \(\mathstrut +\mathstrut 157344642221562801276041757600q^{33} \) \(\mathstrut -\mathstrut 14575908480758621487300381842304q^{34} \) \(\mathstrut +\mathstrut 41100171486790863962401658870544q^{36} \) \(\mathstrut +\mathstrut 5673106137824212681873457220696q^{37} \) \(\mathstrut -\mathstrut 9206461430638842876438079090008q^{39} \) \(\mathstrut +\mathstrut 50495897877443363581635475618560q^{40} \) \(\mathstrut -\mathstrut 939238658319640212873301303645920q^{42} \) \(\mathstrut +\mathstrut 1012654832326802922602871229857576q^{43} \) \(\mathstrut +\mathstrut 196109968512215856818385626472000q^{45} \) \(\mathstrut -\mathstrut 3082500781506234684371181468390336q^{46} \) \(\mathstrut +\mathstrut 6532128822166367998693520969705088q^{48} \) \(\mathstrut +\mathstrut 8498166150175390075155260408801892q^{49} \) \(\mathstrut +\mathstrut 27565453699222767413826960590504832q^{51} \) \(\mathstrut -\mathstrut 57328509042562386918101767400001504q^{52} \) \(\mathstrut -\mathstrut 102847607224782098537542351912875792q^{54} \) \(\mathstrut -\mathstrut 9637639495259752880102706884884800q^{55} \) \(\mathstrut -\mathstrut 40307213604482059940636368892395464q^{57} \) \(\mathstrut +\mathstrut 772129436848561910287203884295052320q^{58} \) \(\mathstrut -\mathstrut 114385571579949295944121547557720320q^{60} \) \(\mathstrut -\mathstrut 494443282701607071691140418439862696q^{61} \) \(\mathstrut +\mathstrut 1379291076525018665154441723571240776q^{63} \) \(\mathstrut -\mathstrut 6231783699524672226208093043936541696q^{64} \) \(\mathstrut +\mathstrut 2652084094607847915810184973553481440q^{66} \) \(\mathstrut +\mathstrut 5401062423529881431761320436868275176q^{67} \) \(\mathstrut +\mathstrut 7110274695178254111533494284632123328q^{69} \) \(\mathstrut +\mathstrut 516103243900107216646679160954379200q^{70} \) \(\mathstrut -\mathstrut 27544975046740790141119542770107057920q^{72} \) \(\mathstrut +\mathstrut 30000154498324943042431295514883418136q^{73} \) \(\mathstrut +\mathstrut 43820294796704764666539599709819928500q^{75} \) \(\mathstrut -\mathstrut 215478934792040263381331019050660960352q^{76} \) \(\mathstrut +\mathstrut 234946633516471169601955850003339878560q^{78} \) \(\mathstrut -\mathstrut 128704557118405295534397879672035334840q^{79} \) \(\mathstrut +\mathstrut 473157359902659920298963194247360443532q^{81} \) \(\mathstrut -\mathstrut 639159997421964256448917103585883414720q^{82} \) \(\mathstrut +\mathstrut 1283288903941350744781821238287455403552q^{84} \) \(\mathstrut -\mathstrut 1077142486191382871466217243736209678080q^{85} \) \(\mathstrut +\mathstrut 1076668306862385320797179121273520148960q^{87} \) \(\mathstrut -\mathstrut 2918662713596496795370587920448329114880q^{88} \) \(\mathstrut +\mathstrut 6571793457940570799819318674019816438880q^{90} \) \(\mathstrut -\mathstrut 9859184204686878150356379414618151910256q^{91} \) \(\mathstrut +\mathstrut 11506410044121210986218054652959643683416q^{93} \) \(\mathstrut -\mathstrut 16857264118330945289191940748512432348544q^{94} \) \(\mathstrut +\mathstrut 53068562519213731340201280418423192237056q^{96} \) \(\mathstrut -\mathstrut 41841010071967618660163746722085070705064q^{97} \) \(\mathstrut +\mathstrut 54341076855402233475300783474292013590080q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{41}^{\mathrm{new}}(3, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3.41.b.a \(12\) \(30.403\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-372082572\) \(0\) \(-9\!\cdots\!84\) \(q+\beta _{1}q^{2}+(-31006881-471\beta _{1}+\cdots)q^{3}+\cdots\)