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Properties

Label 5.21.c
Level $5$
Weight $21$
Character orbit 5.c
Rep. character $\chi_{5}(2,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $18$
Newform subspaces $1$
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: \(\Q(i)\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{21}^{\mathrm{new}}(5, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5.21.c.a 5.c 5.c $18$ $12.676$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(-2\) \(29448\) \(-7302140\) \(-585532752\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{2}+(1636-\beta _{2}-1636\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)