# Properties

 Label 288.1.t Level $288$ Weight $1$ Character orbit 288.t Rep. character $\chi_{288}(79,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $2$ Newform subspaces $1$ Sturm bound $48$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$288 = 2^{5} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 288.t (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$72$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$48$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(288, [\chi])$$.

Total New Old
Modular forms 24 6 18
Cusp forms 8 2 6
Eisenstein series 16 4 12

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 0 0

## Trace form

 $$2 q + q^{3} - q^{9} + O(q^{10})$$ $$2 q + q^{3} - q^{9} - q^{11} - 2 q^{17} + 2 q^{19} - q^{25} - 2 q^{27} + q^{33} + q^{41} - q^{43} - q^{49} - q^{51} + q^{57} - q^{59} - q^{67} - 2 q^{73} + q^{75} - q^{81} + 2 q^{83} + 4 q^{89} + q^{97} + 2 q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(288, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
288.1.t.a $$2$$ $$0.144$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$1$$ $$0$$ $$0$$ $$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+\zeta_{6}^{2}q^{11}-q^{17}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(288, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(288, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 3}$$