# Properties

 Label 280.2.s Level $280$ Weight $2$ Character orbit 280.s Rep. character $\chi_{280}(13,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $88$ Newform subspaces $3$ Sturm bound $96$ Trace bound $2$

# Related objects

## Defining parameters

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

## Dimensions

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

Total New Old
Modular forms 104 104 0
Cusp forms 88 88 0
Eisenstein series 16 16 0

## Trace form

 $$88q - 4q^{2} - 4q^{7} - 16q^{8} + O(q^{10})$$ $$88q - 4q^{2} - 4q^{7} - 16q^{8} - 8q^{15} - 24q^{16} - 8q^{18} + 4q^{22} - 8q^{23} - 8q^{25} - 4q^{28} - 44q^{30} - 24q^{32} + 24q^{36} + 40q^{42} + 16q^{46} - 60q^{50} + 32q^{56} + 16q^{57} - 68q^{58} + 32q^{60} + 12q^{63} - 8q^{65} + 16q^{70} - 80q^{71} + 80q^{72} - 132q^{78} - 72q^{81} - 72q^{86} + 48q^{88} - 24q^{92} + 80q^{95} + 40q^{98} + O(q^{100})$$

## 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.s.a $$8$$ $$2.236$$ 8.0.$$\cdots$$.8 $$\Q(\sqrt{-14})$$ $$-8$$ $$0$$ $$0$$ $$0$$ $$q+(-1-\beta _{3})q^{2}+(-\beta _{1}-\beta _{4})q^{3}+2\beta _{3}q^{4}+\cdots$$
280.2.s.b $$8$$ $$2.236$$ 8.0.$$\cdots$$.8 $$\Q(\sqrt{-14})$$ $$8$$ $$0$$ $$0$$ $$0$$ $$q+(1+\beta _{4})q^{2}+\beta _{1}q^{3}+2\beta _{4}q^{4}-\beta _{5}q^{5}+\cdots$$
280.2.s.c $$72$$ $$2.236$$ None $$-4$$ $$0$$ $$0$$ $$-4$$