# Properties

 Label 216.3.m Level $216$ Weight $3$ Character orbit 216.m Rep. character $\chi_{216}(17,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $12$ 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.m (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{6})$$ 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 168 12 156
Cusp forms 120 12 108
Eisenstein series 48 0 48

## Trace form

 $$12q + O(q^{10})$$ $$12q - 18q^{11} + 12q^{19} + 72q^{23} + 30q^{25} + 108q^{29} + 24q^{31} - 126q^{41} - 18q^{43} - 324q^{47} - 18q^{49} - 24q^{55} + 126q^{59} - 48q^{61} + 432q^{65} - 42q^{67} - 36q^{73} - 504q^{77} - 60q^{79} - 180q^{83} - 48q^{85} - 192q^{91} + 828q^{95} + 6q^{97} + O(q^{100})$$

## 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.m.a $$4$$ $$5.886$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$-6$$ $$-6$$ $$q+(-1+\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}-3\beta _{2}+\cdots)q^{7}+\cdots$$
216.3.m.b $$8$$ $$5.886$$ 8.0.$$\cdots$$.9 None $$0$$ $$0$$ $$6$$ $$6$$ $$q+(1-\beta _{1}-\beta _{2}+\beta _{4})q^{5}+(1-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(216, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(216, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(9, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(27, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(54, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(108, [\chi])$$$$^{\oplus 2}$$