# Properties

 Label 324.2.m Level $324$ Weight $2$ Character orbit 324.m Rep. character $\chi_{324}(13,\cdot)$ Character field $\Q(\zeta_{27})$ Dimension $162$ Newform subspaces $1$ Sturm bound $108$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$324 = 2^{2} \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 324.m (of order $$27$$ and degree $$18$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$81$$ Character field: $$\Q(\zeta_{27})$$ Newform subspaces: $$1$$ Sturm bound: $$108$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(324, [\chi])$$.

Total New Old
Modular forms 1026 162 864
Cusp forms 918 162 756
Eisenstein series 108 0 108

## Trace form

 $$162q + O(q^{10})$$ $$162q + 27q^{21} + 27q^{23} + 27q^{27} + 27q^{29} + 27q^{33} + 27q^{35} - 18q^{41} - 54q^{45} - 54q^{47} - 63q^{51} - 54q^{53} - 54q^{57} - 63q^{59} - 54q^{63} - 90q^{65} + 27q^{67} - 90q^{69} - 72q^{71} - 90q^{75} - 144q^{77} + 54q^{79} - 72q^{81} - 72q^{83} + 54q^{85} - 144q^{87} - 99q^{89} - 90q^{93} - 126q^{95} + 27q^{97} - 90q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(324, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
324.2.m.a $$162$$ $$2.587$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(324, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(324, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(81, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(162, [\chi])$$$$^{\oplus 2}$$