Properties

 Label 280.1.bi Level $280$ Weight $1$ Character orbit 280.bi Rep. character $\chi_{280}(179,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $4$ Newform subspaces $2$ Sturm bound $48$ Trace bound $2$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$280 = 2^{3} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 280.bi (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$280$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$48$$ Trace bound: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(280, [\chi])$$.

Total New Old
Modular forms 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 0

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 4 0 0 0

Trace form

 $$4q - 2q^{4} - 2q^{9} + O(q^{10})$$ $$4q - 2q^{4} - 2q^{9} - 2q^{10} + 2q^{11} - 2q^{14} - 2q^{16} + 2q^{19} - 2q^{25} + 2q^{26} - 2q^{35} + 4q^{36} - 2q^{40} - 4q^{41} + 2q^{44} + 2q^{46} + 4q^{49} + 4q^{56} - 4q^{59} + 4q^{64} + 2q^{65} + 2q^{74} - 4q^{76} - 2q^{81} - 4q^{89} + 4q^{90} - 4q^{91} + 2q^{94} - 4q^{99} + O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(280, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
280.1.bi.a $$2$$ $$0.140$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-10})$$ None $$-1$$ $$0$$ $$-1$$ $$2$$ $$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+q^{7}+\cdots$$
280.1.bi.b $$2$$ $$0.140$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-10})$$ None $$1$$ $$0$$ $$1$$ $$-2$$ $$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}-q^{7}+\cdots$$