# Properties

 Label 280.2.g Level $280$ Weight $2$ Character orbit 280.g Rep. character $\chi_{280}(169,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $2$ Sturm bound $96$ Trace bound $1$

# Related objects

## Defining parameters

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

## Dimensions

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

Total New Old
Modular forms 56 8 48
Cusp forms 40 8 32
Eisenstein series 16 0 16

## Trace form

 $$8 q + 4 q^{5} - 4 q^{9} + O(q^{10})$$ $$8 q + 4 q^{5} - 4 q^{9} + 12 q^{11} - 16 q^{15} - 4 q^{21} - 4 q^{25} - 4 q^{29} + 8 q^{31} + 12 q^{39} + 16 q^{41} - 20 q^{45} - 8 q^{49} + 36 q^{51} - 16 q^{55} - 24 q^{59} + 40 q^{61} - 24 q^{65} - 40 q^{69} - 24 q^{71} - 32 q^{75} - 12 q^{79} + 32 q^{81} + 20 q^{85} - 24 q^{89} + 12 q^{91} + 12 q^{95} - 8 q^{99} + O(q^{100})$$

## 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.g.a $2$ $2.236$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+iq^{3}+(2-i)q^{5}+iq^{7}+2q^{9}-q^{11}+\cdots$$
280.2.g.b $6$ $2.236$ 6.0.5161984.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{3}+(\beta _{1}-\beta _{5})q^{5}+\beta _{4}q^{7}+(-1+\cdots)q^{9}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(280, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 2}$$