# Properties

 Label 288.4.d Level $288$ Weight $4$ Character orbit 288.d Rep. character $\chi_{288}(145,\cdot)$ Character field $\Q$ Dimension $14$ Newform subspaces $4$ Sturm bound $192$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$288 = 2^{5} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 288.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$192$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(288, [\chi])$$.

Total New Old
Modular forms 160 16 144
Cusp forms 128 14 114
Eisenstein series 32 2 30

## Trace form

 $$14 q + 16 q^{7} + O(q^{10})$$ $$14 q + 16 q^{7} - 24 q^{17} + 24 q^{23} - 274 q^{25} + 80 q^{31} - 96 q^{41} + 264 q^{47} + 750 q^{49} + 48 q^{55} + 624 q^{65} - 1848 q^{71} - 156 q^{73} - 2144 q^{79} - 312 q^{89} + 4320 q^{95} - 1084 q^{97} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(288, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
288.4.d.a $2$ $16.993$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$16$$ $$q-2\beta q^{5}+8q^{7}+3\beta q^{11}-10\beta q^{13}+\cdots$$
288.4.d.b $2$ $16.993$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-6})$$ $$0$$ $$0$$ $$0$$ $$68$$ $$q+7\beta q^{5}+34q^{7}+2\beta q^{11}-267q^{25}+\cdots$$
288.4.d.c $4$ $16.993$ $$\Q(\sqrt{-10}, \sqrt{22})$$ None $$0$$ $$0$$ $$0$$ $$-40$$ $$q+\beta _{1}q^{5}-10q^{7}-6\beta _{1}q^{11}+\beta _{3}q^{13}+\cdots$$
288.4.d.d $6$ $16.993$ 6.0.8248384.1 None $$0$$ $$0$$ $$0$$ $$-28$$ $$q-\beta _{2}q^{5}+(-5-\beta _{1})q^{7}+(-2\beta _{2}-2\beta _{3}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(288, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(288, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(8, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 2}$$