# Properties

 Label 216.3.r Level $216$ Weight $3$ Character orbit 216.r Rep. character $\chi_{216}(43,\cdot)$ Character field $\Q(\zeta_{18})$ Dimension $420$ Newform subspaces $2$ Sturm bound $108$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$216 = 2^{3} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 216.r (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$216$$ Character field: $$\Q(\zeta_{18})$$ Newform subspaces: $$2$$ Sturm bound: $$108$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(216, [\chi])$$.

Total New Old
Modular forms 444 444 0
Cusp forms 420 420 0
Eisenstein series 24 24 0

## Trace form

 $$420q - 6q^{2} - 12q^{3} - 6q^{4} - 6q^{6} - 3q^{8} - 12q^{9} + O(q^{10})$$ $$420q - 6q^{2} - 12q^{3} - 6q^{4} - 6q^{6} - 3q^{8} - 12q^{9} - 3q^{10} - 12q^{11} + 39q^{12} - 51q^{14} - 6q^{16} - 6q^{17} + 15q^{18} - 6q^{19} - 69q^{20} - 6q^{22} - 84q^{24} - 12q^{25} + 150q^{26} - 12q^{27} - 12q^{28} + 141q^{30} + 84q^{32} + 12q^{33} + 6q^{34} - 6q^{35} - 36q^{36} - 84q^{38} - 81q^{40} + 60q^{41} - 546q^{42} - 12q^{43} + 213q^{44} - 3q^{46} + 207q^{48} - 12q^{49} - 315q^{50} + 42q^{51} - 33q^{52} + 78q^{54} - 405q^{56} + 42q^{57} - 141q^{58} + 420q^{59} - 882q^{60} + 294q^{62} - 3q^{64} - 12q^{65} + 393q^{66} - 12q^{67} - 525q^{68} - 141q^{70} + 228q^{72} - 6q^{73} - 207q^{74} - 348q^{75} + 42q^{76} - 216q^{78} + 798q^{80} - 12q^{81} - 12q^{82} - 732q^{83} + 654q^{84} + 282q^{86} + 186q^{88} - 6q^{89} - 420q^{90} - 6q^{91} - 1077q^{92} + 345q^{94} - 1242q^{96} - 12q^{97} - 516q^{98} - 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(216, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
216.3.r.a $$12$$ $$5.886$$ 12.0.$$\cdots$$.1 $$\Q(\sqrt{-2})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\beta _{2}q^{2}+(\beta _{5}-\beta _{8}-\beta _{11})q^{3}+4\beta _{4}q^{4}+\cdots$$
216.3.r.b $$408$$ $$5.886$$ None $$-6$$ $$-12$$ $$0$$ $$0$$