# Properties

 Label 288.2.r Level $288$ Weight $2$ Character orbit 288.r Rep. character $\chi_{288}(49,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $20$ Newform subspaces $2$ Sturm bound $96$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$288 = 2^{5} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 288.r (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$72$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$96$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 112 28 84
Cusp forms 80 20 60
Eisenstein series 32 8 24

## Trace form

 $$20q + 2q^{7} - 4q^{9} + O(q^{10})$$ $$20q + 2q^{7} - 4q^{9} + 10q^{15} - 8q^{17} + 14q^{23} + 2q^{31} - 18q^{33} - 2q^{39} + 2q^{41} - 18q^{47} + 28q^{55} + 4q^{57} - 50q^{63} - 22q^{65} - 48q^{71} - 8q^{73} + 2q^{79} - 8q^{81} - 42q^{87} + 8q^{89} - 40q^{95} - 2q^{97} + O(q^{100})$$

## 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.r.a $$4$$ $$2.300$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+2\zeta_{12}q^{5}+4\zeta_{12}^{2}q^{7}+\cdots$$
288.2.r.b $$16$$ $$2.300$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-6$$ $$q-\beta _{12}q^{3}+(-\beta _{4}-\beta _{7}+\beta _{8}-\beta _{11}+\cdots)q^{5}+\cdots$$

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

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