# Properties

 Label 162.2.e Level $162$ Weight $2$ Character orbit 162.e Rep. character $\chi_{162}(19,\cdot)$ Character field $\Q(\zeta_{9})$ Dimension $18$ Newform subspaces $2$ Sturm bound $54$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$162 = 2 \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 162.e (of order $$9$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$27$$ Character field: $$\Q(\zeta_{9})$$ Newform subspaces: $$2$$ Sturm bound: $$54$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(162, [\chi])$$.

Total New Old
Modular forms 198 18 180
Cusp forms 126 18 108
Eisenstein series 72 0 72

## Trace form

 $$18 q + 6 q^{5} + 3 q^{8} + O(q^{10})$$ $$18 q + 6 q^{5} + 3 q^{8} + 15 q^{11} + 6 q^{14} + 12 q^{17} - 12 q^{20} - 9 q^{22} - 24 q^{23} - 18 q^{25} - 36 q^{26} - 30 q^{29} - 18 q^{31} - 9 q^{34} - 6 q^{35} + 12 q^{38} + 15 q^{41} - 9 q^{43} + 6 q^{44} - 18 q^{49} + 36 q^{50} + 24 q^{53} + 6 q^{56} - 6 q^{59} - 18 q^{61} + 24 q^{62} - 9 q^{64} - 6 q^{65} + 27 q^{67} + 12 q^{68} + 36 q^{70} - 24 q^{71} - 18 q^{73} - 30 q^{74} + 18 q^{76} - 42 q^{77} + 72 q^{79} - 12 q^{80} + 72 q^{85} - 27 q^{86} + 18 q^{88} + 3 q^{89} - 18 q^{91} - 6 q^{92} + 36 q^{94} - 6 q^{95} + 27 q^{97} + 15 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(162, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
162.2.e.a $6$ $1.294$ $$\Q(\zeta_{18})$$ None $$0$$ $$0$$ $$3$$ $$3$$ $$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}-\zeta_{18}^{5}q^{4}+(\zeta_{18}^{2}+\cdots)q^{5}+\cdots$$
162.2.e.b $12$ $1.294$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$3$$ $$-3$$ $$q+(\beta _{4}+\beta _{8})q^{2}-\beta _{6}q^{4}+(1-\beta _{2}+\beta _{7}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(162, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(162, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(27, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(54, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(81, [\chi])$$$$^{\oplus 2}$$