# Properties

 Label 280.2.b Level $280$ Weight $2$ Character orbit 280.b Rep. character $\chi_{280}(141,\cdot)$ Character field $\Q$ Dimension $24$ Newform subspaces $4$ Sturm bound $96$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$280 = 2^{3} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 280.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$96$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$, $$13$$

## Dimensions

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

Total New Old
Modular forms 52 24 28
Cusp forms 44 24 20
Eisenstein series 8 0 8

## Trace form

 $$24q + 2q^{2} + 2q^{4} - 8q^{6} + 4q^{7} + 14q^{8} - 24q^{9} + O(q^{10})$$ $$24q + 2q^{2} + 2q^{4} - 8q^{6} + 4q^{7} + 14q^{8} - 24q^{9} - 4q^{10} - 12q^{12} - 2q^{14} - 8q^{15} - 14q^{16} + 2q^{18} + 8q^{22} + 16q^{23} - 20q^{24} - 24q^{25} - 4q^{26} + 10q^{28} + 16q^{30} + 16q^{31} - 18q^{32} - 16q^{33} - 8q^{34} - 2q^{36} + 20q^{38} - 48q^{39} + 16q^{40} + 16q^{41} + 36q^{44} - 32q^{46} + 44q^{48} + 24q^{49} - 2q^{50} + 24q^{52} + 36q^{54} - 2q^{56} + 16q^{57} - 12q^{58} + 4q^{60} - 16q^{62} - 20q^{63} + 2q^{64} + 68q^{66} - 76q^{68} + 8q^{71} - 22q^{72} - 8q^{74} - 20q^{76} + 4q^{78} + 24q^{79} + 8q^{81} - 52q^{82} + 28q^{84} - 68q^{86} + 48q^{87} - 36q^{88} + 16q^{90} + 20q^{94} - 32q^{95} + 12q^{96} + 2q^{98} + O(q^{100})$$

## 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.b.a $$2$$ $$2.236$$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$0$$ $$-2$$ $$q+(1+i)q^{2}+2iq^{3}+2iq^{4}-iq^{5}+\cdots$$
280.2.b.b $$2$$ $$2.236$$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$0$$ $$2$$ $$q+(1+i)q^{2}+2iq^{3}+2iq^{4}+iq^{5}+\cdots$$
280.2.b.c $$8$$ $$2.236$$ 8.0.18939904.2 None $$0$$ $$0$$ $$0$$ $$-8$$ $$q-\beta _{6}q^{2}+(-\beta _{5}+\beta _{7})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots$$
280.2.b.d $$12$$ $$2.236$$ 12.0.$$\cdots$$.1 None $$-2$$ $$0$$ $$0$$ $$12$$ $$q+\beta _{6}q^{2}+(\beta _{1}-\beta _{3}+\beta _{7})q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(280, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 2}$$