# Properties

 Label 216.2.l Level $216$ Weight $2$ Character orbit 216.l Rep. character $\chi_{216}(35,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $20$ Newform subspaces $2$ Sturm bound $72$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$216 = 2^{3} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 216.l (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$72$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$72$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(216, [\chi])$$.

Total New Old
Modular forms 84 28 56
Cusp forms 60 20 40
Eisenstein series 24 8 16

## Trace form

 $$20 q + 3 q^{2} - q^{4} + O(q^{10})$$ $$20 q + 3 q^{2} - q^{4} + 6 q^{11} + 18 q^{14} - q^{16} - 8 q^{19} - 18 q^{20} - 5 q^{22} - 4 q^{25} - 12 q^{28} - 27 q^{32} - 5 q^{34} - 21 q^{38} - 12 q^{40} + 18 q^{41} - 2 q^{43} + 12 q^{46} - 4 q^{49} - 51 q^{50} - 18 q^{52} + 66 q^{56} + 12 q^{58} - 30 q^{59} + 2 q^{64} + 6 q^{65} - 2 q^{67} + 45 q^{68} + 18 q^{70} - 8 q^{73} + 60 q^{74} - 11 q^{76} + 10 q^{82} - 54 q^{83} + 87 q^{86} - 5 q^{88} - 36 q^{91} - 84 q^{92} + 24 q^{94} - 2 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(216, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
216.2.l.a $$4$$ $$1.725$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ $$\Q(\sqrt{-2})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+2\beta _{3}q^{8}+(3-\beta _{1}+\cdots)q^{11}+\cdots$$
216.2.l.b $$16$$ $$1.725$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$3$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{11}q^{2}+(-1-\beta _{1}+\beta _{2}-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(216, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(216, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 2}$$