# Properties

 Label 280.2.l Level $280$ Weight $2$ Character orbit 280.l Rep. character $\chi_{280}(29,\cdot)$ Character field $\Q$ Dimension $36$ 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.l (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$40$$ Character field: $$\Q$$ 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 52 36 16
Cusp forms 44 36 8
Eisenstein series 8 0 8

## Trace form

 $$36q + 4q^{4} - 4q^{6} + 36q^{9} + O(q^{10})$$ $$36q + 4q^{4} - 4q^{6} + 36q^{9} - 8q^{10} + 20q^{16} - 24q^{20} - 48q^{24} + 4q^{25} - 4q^{26} + 4q^{30} - 16q^{31} + 12q^{34} - 20q^{36} - 32q^{39} + 16q^{40} - 8q^{41} + 56q^{44} - 36q^{49} - 12q^{50} - 52q^{54} - 32q^{55} + 12q^{56} - 20q^{60} - 20q^{64} - 24q^{65} - 28q^{66} - 12q^{70} + 56q^{71} - 24q^{74} + 48q^{76} + 24q^{79} + 64q^{80} + 36q^{81} + 24q^{86} - 40q^{89} - 52q^{90} - 92q^{94} + 40q^{95} + 48q^{96} + O(q^{100})$$

## 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.l.a $$36$$ $$2.236$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(280, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 2}$$