# Properties

 Label 162.2.c Level $162$ Weight $2$ Character orbit 162.c Rep. character $\chi_{162}(55,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $8$ Newform subspaces $4$ Sturm bound $54$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$162 = 2 \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 162.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$4$$ Sturm bound: $$54$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

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

Total New Old
Modular forms 78 8 70
Cusp forms 30 8 22
Eisenstein series 48 0 48

## Trace form

 $$8 q - 4 q^{4} + 10 q^{7} + O(q^{10})$$ $$8 q - 4 q^{4} + 10 q^{7} + 10 q^{13} - 4 q^{16} - 8 q^{19} - 6 q^{22} - 16 q^{25} - 20 q^{28} - 2 q^{31} - 6 q^{34} + 4 q^{37} + 4 q^{43} + 24 q^{46} - 6 q^{49} + 10 q^{52} - 36 q^{55} + 30 q^{58} - 14 q^{61} + 8 q^{64} - 20 q^{67} + 18 q^{70} + 16 q^{73} + 4 q^{76} + 16 q^{79} - 18 q^{85} - 6 q^{88} + 32 q^{91} - 12 q^{94} - 2 q^{97} + O(q^{100})$$

## 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.c.a $2$ $1.294$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-3$$ $$4$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots$$
162.2.c.b $2$ $1.294$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$3$$ $$1$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots$$
162.2.c.c $2$ $1.294$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-3$$ $$1$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots$$
162.2.c.d $2$ $1.294$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$3$$ $$4$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(162, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(54, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(81, [\chi])$$$$^{\oplus 2}$$