# Properties

 Label 224.2.i Level $224$ Weight $2$ Character orbit 224.i Rep. character $\chi_{224}(65,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $16$ Newform subspaces $4$ Sturm bound $64$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$224 = 2^{5} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 224.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$4$$ Sturm bound: $$64$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(224, [\chi])$$.

Total New Old
Modular forms 80 16 64
Cusp forms 48 16 32
Eisenstein series 32 0 32

## Trace form

 $$16 q - 8 q^{9} + O(q^{10})$$ $$16 q - 8 q^{9} - 16 q^{13} + 24 q^{21} - 16 q^{25} + 16 q^{29} - 8 q^{33} + 8 q^{37} + 16 q^{41} - 8 q^{45} - 16 q^{49} - 8 q^{53} - 48 q^{57} - 24 q^{61} + 8 q^{65} + 24 q^{73} - 48 q^{77} + 32 q^{81} - 80 q^{85} + 40 q^{89} + 8 q^{93} - 16 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(224, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
224.2.i.a $4$ $1.789$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$-2$$ $$-2$$ $$-4$$ $$q+(-1+\beta _{1}-\beta _{2})q^{3}+(-2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
224.2.i.b $4$ $1.789$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-1+\zeta_{12}^{2}+\cdots)q^{5}+\cdots$$
224.2.i.c $4$ $1.789$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$0$$ $$0$$ $$6$$ $$0$$ $$q+\beta _{1}q^{3}-3\beta _{2}q^{5}-\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots$$
224.2.i.d $4$ $1.789$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$2$$ $$-2$$ $$4$$ $$q+(1+\beta _{1}+\beta _{2})q^{3}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(224, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(224, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(112, [\chi])$$$$^{\oplus 2}$$