# Properties

 Label 560.1.bt Level $560$ Weight $1$ Character orbit 560.bt Rep. character $\chi_{560}(79,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $4$ Newform subspaces $1$ Sturm bound $96$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$560 = 2^{4} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 560.bt (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$140$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$96$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(560, [\chi])$$.

Total New Old
Modular forms 40 4 36
Cusp forms 16 4 12
Eisenstein series 24 0 24

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

 $$4q + 2q^{5} - 4q^{9} + O(q^{10})$$ $$4q + 2q^{5} - 4q^{9} - 6q^{21} - 2q^{25} - 4q^{29} + 4q^{41} + 4q^{45} + 2q^{49} - 2q^{61} + 12q^{69} - 2q^{81} + 2q^{89} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(560, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
560.1.bt.a $$4$$ $$0.279$$ $$\Q(\zeta_{12})$$ $$D_{6}$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{3}+\zeta_{12}^{2}q^{5}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(560, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(560, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 3}$$