# Properties

 Label 288.2.f Level $288$ Weight $2$ Character orbit 288.f Rep. character $\chi_{288}(143,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $1$ Sturm bound $96$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$288 = 2^{5} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 288.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$24$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$96$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(288, [\chi])$$.

Total New Old
Modular forms 64 4 60
Cusp forms 32 4 28
Eisenstein series 32 0 32

## Trace form

 $$4q + O(q^{10})$$ $$4q + 16q^{19} + 4q^{25} - 32q^{43} - 20q^{49} + 16q^{67} - 16q^{73} - 48q^{91} + 32q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(288, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
288.2.f.a $$4$$ $$2.300$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{5}-\beta _{3}q^{7}-2\beta _{1}q^{11}-\beta _{3}q^{13}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(288, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(288, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 2}$$