# Properties

 Label 280.2.x Level $280$ Weight $2$ Character orbit 280.x Rep. character $\chi_{280}(97,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $24$ Newform subspaces $1$ Sturm bound $96$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$280 = 2^{3} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 280.x (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$96$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(280, [\chi])$$.

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

## Trace form

 $$24q + 4q^{7} + O(q^{10})$$ $$24q + 4q^{7} + 8q^{11} - 8q^{15} + 16q^{21} - 32q^{23} + 8q^{25} + 12q^{35} - 8q^{37} + 16q^{43} - 24q^{51} - 16q^{53} + 20q^{63} - 48q^{65} - 32q^{67} - 32q^{71} - 40q^{77} - 72q^{81} + 16q^{85} - 64q^{91} + 72q^{93} - 24q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(280, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
280.2.x.a $$24$$ $$2.236$$ None $$0$$ $$0$$ $$0$$ $$4$$

## Decomposition of $$S_{2}^{\mathrm{old}}(280, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(280, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 2}$$