Properties

Label 5.21.c
Level 5
Weight 21
Character orbit c
Rep. character \(\chi_{5}(2,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 18
Newforms 1
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 21 \)
Character orbit: \([\chi]\) = 5.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(5, [\chi])\).

Total New Old
Modular forms 22 22 0
Cusp forms 18 18 0
Eisenstein series 4 4 0

Trace form

\( 18q - 2q^{2} + 29448q^{3} - 7302140q^{5} + 19792536q^{6} - 585532752q^{7} + 930113700q^{8} + O(q^{10}) \) \( 18q - 2q^{2} + 29448q^{3} - 7302140q^{5} + 19792536q^{6} - 585532752q^{7} + 930113700q^{8} - 17138778090q^{10} - 6506343064q^{11} + 140311795848q^{12} - 369354655602q^{13} + 998626204320q^{15} - 6345876020232q^{16} + 6508314764998q^{17} - 11265991705902q^{18} + 38356516779780q^{20} - 97402974719064q^{21} + 161054386758096q^{22} - 81655963656152q^{23} + 33913283845350q^{25} + 234104101103636q^{26} - 511935279143400q^{27} + 772213614545352q^{28} - 877127470680480q^{30} + 1742256896900736q^{31} - 4072699683722552q^{32} + 1579138514189496q^{33} - 4817791288113440q^{35} + 2214548622647868q^{36} + 6383289895587498q^{37} - 14134212502378200q^{38} + 43297629431150700q^{40} - 30602304597564664q^{41} + 48810732785962896q^{42} - 46399469942287752q^{43} + 67947826451186070q^{45} + 17467214047538136q^{46} - 137109249757437752q^{47} - 103698596104819152q^{48} - 40012852869983150q^{50} + 686047946059669536q^{51} - 745026624616846452q^{52} - 184102027021671302q^{53} + 752956242406989720q^{55} + 685775432394721200q^{56} - 785021725278622800q^{57} - 2701246502184220800q^{58} + 6219197632829342760q^{60} + 49879194030044136q^{61} - 1190554579738283704q^{62} - 7082176979112100152q^{63} + 6907070599410641170q^{65} + 11227963704975799872q^{66} - 5597336519263153752q^{67} - 25617328014464685148q^{68} + 31706333959370270760q^{70} + 10983277495574224736q^{71} - 41525052650392592700q^{72} - 19072400700441139902q^{73} + 36766882672050433200q^{75} + 75630007803532292400q^{76} - 47766064678699704904q^{77} - 109239984515466629304q^{78} + 134231700802559812960q^{80} + 74219234884008322518q^{81} - 83501540658117625104q^{82} - 119739383617210903952q^{83} + 169044713294843560110q^{85} + 33497378050769887736q^{86} - 28944830404542403200q^{87} - 337125565675837197600q^{88} + 396784292056608506070q^{90} + 86281377644254817136q^{91} - 206921051460419061752q^{92} - 285487695991878257304q^{93} + 118106834336527303800q^{95} + 377091713708556287136q^{96} - 318608382222604685502q^{97} - 27697031317753120498q^{98} + O(q^{100}) \)

Decomposition of \(S_{21}^{\mathrm{new}}(5, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5.21.c.a \(18\) \(12.676\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(-2\) \(29448\) \(-7302140\) \(-585532752\) \(q-\beta _{1}q^{2}+(1636-\beta _{2}-1636\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)