# Properties

 Label 320.2.o Level $320$ Weight $2$ Character orbit 320.o Rep. character $\chi_{320}(223,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $24$ Newform subspaces $6$ Sturm bound $96$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$320 = 2^{6} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 320.o (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$40$$ Character field: $$\Q(i)$$ Newform subspaces: $$6$$ Sturm bound: $$96$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(320, [\chi])$$.

Total New Old
Modular forms 120 24 96
Cusp forms 72 24 48
Eisenstein series 48 0 48

## Trace form

 $$24 q + O(q^{10})$$ $$24 q + 24 q^{17} - 24 q^{25} - 24 q^{65} - 24 q^{73} - 120 q^{81} - 120 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(320, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
320.2.o.a $2$ $2.555$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$-2$$ $$-2$$ $$q+(-1+i)q^{3}+(-1-2i)q^{5}+(-1+\cdots)q^{7}+\cdots$$
320.2.o.b $2$ $2.555$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$2$$ $$2$$ $$q+(-1+i)q^{3}+(1+2i)q^{5}+(1-i)q^{7}+\cdots$$
320.2.o.c $2$ $2.555$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$-2$$ $$2$$ $$q+(1-i)q^{3}+(-1-2i)q^{5}+(1-i)q^{7}+\cdots$$
320.2.o.d $2$ $2.555$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$2$$ $$-2$$ $$q+(1-i)q^{3}+(1+2i)q^{5}+(-1+i)q^{7}+\cdots$$
320.2.o.e $8$ $2.555$ 8.0.49787136.1 None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+(-\beta _{2}-\beta _{7})q^{3}+\beta _{7}q^{5}-\beta _{6}q^{7}+\cdots$$
320.2.o.f $8$ $2.555$ 8.0.49787136.1 None $$0$$ $$0$$ $$0$$ $$4$$ $$q+(-\beta _{2}-\beta _{7})q^{3}-\beta _{7}q^{5}+\beta _{6}q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(320, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(320, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(160, [\chi])$$$$^{\oplus 2}$$