# Properties

 Label 320.2.j Level $320$ Weight $2$ Character orbit 320.j Rep. character $\chi_{320}(47,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $20$ Newform subspaces $2$ Sturm bound $96$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$320 = 2^{6} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 320.j (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$80$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$96$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

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

## Trace form

 $$20 q - 2 q^{5} + 4 q^{7} - 12 q^{9} + O(q^{10})$$ $$20 q - 2 q^{5} + 4 q^{7} - 12 q^{9} + 4 q^{11} - 4 q^{13} - 12 q^{15} - 4 q^{17} - 8 q^{19} - 4 q^{21} + 4 q^{23} - 4 q^{33} - 4 q^{37} + 36 q^{43} - 6 q^{45} + 24 q^{47} - 4 q^{51} + 4 q^{55} + 12 q^{57} + 16 q^{59} + 12 q^{61} - 12 q^{63} - 4 q^{65} - 20 q^{67} + 28 q^{69} - 24 q^{71} + 8 q^{73} - 48 q^{75} - 20 q^{81} - 12 q^{85} - 52 q^{87} - 12 q^{91} + 8 q^{93} + 40 q^{95} - 4 q^{97} + 20 q^{99} + O(q^{100})$$

## 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.j.a $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$6$$ $$q-2iq^{3}+(1+2i)q^{5}+(3+3i)q^{7}+\cdots$$
320.2.j.b $$18$$ $$2.555$$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None $$0$$ $$0$$ $$-4$$ $$-2$$ $$q-\beta _{12}q^{3}-\beta _{4}q^{5}+\beta _{10}q^{7}+(-1+\cdots)q^{9}+\cdots$$

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

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