# Properties

 Label 288.2.i Level $288$ Weight $2$ Character orbit 288.i Rep. character $\chi_{288}(97,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $24$ Newform subspaces $6$ Sturm bound $96$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$288 = 2^{5} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 288.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$6$$ Sturm bound: $$96$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

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

Total New Old
Modular forms 112 24 88
Cusp forms 80 24 56
Eisenstein series 32 0 32

## Trace form

 $$24 q + 4 q^{9} + O(q^{10})$$ $$24 q + 4 q^{9} + 8 q^{17} + 8 q^{21} - 12 q^{25} - 8 q^{29} + 28 q^{33} + 12 q^{41} - 40 q^{45} - 12 q^{49} - 48 q^{53} - 4 q^{57} - 16 q^{65} - 48 q^{69} + 24 q^{73} - 16 q^{77} - 68 q^{81} - 64 q^{89} + 64 q^{93} - 12 q^{97} + O(q^{100})$$

## 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.i.a $2$ $2.300$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$-4$$ $$-2$$ $$q+(-1-\zeta_{6})q^{3}-4\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots$$
288.2.i.b $2$ $2.300$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$-4$$ $$2$$ $$q+(1+\zeta_{6})q^{3}-4\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots$$
288.2.i.c $4$ $2.300$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$-4$$ $$2$$ $$2$$ $$q+(-1+\beta _{3})q^{3}+\beta _{2}q^{5}+(1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$$
288.2.i.d $4$ $2.300$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\zeta_{12}^{3}q^{3}+(1-\zeta_{12})q^{5}+\zeta_{12}^{2}q^{7}+\cdots$$
288.2.i.e $4$ $2.300$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$4$$ $$2$$ $$-2$$ $$q+(1-\beta _{3})q^{3}+(1-\beta _{2})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$$
288.2.i.f $8$ $2.300$ 8.0.170772624.1 None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(-\beta _{1}+\beta _{5})q^{3}+(1-\beta _{4}+\beta _{7})q^{5}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(288, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 2}$$