# 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

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

## 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

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