# Properties

 Label 560.2.bw Level $560$ Weight $2$ Character orbit 560.bw Rep. character $\chi_{560}(289,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $44$ Newform subspaces $6$ Sturm bound $192$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$560 = 2^{4} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 560.bw (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$6$$ Sturm bound: $$192$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(560, [\chi])$$.

Total New Old
Modular forms 216 52 164
Cusp forms 168 44 124
Eisenstein series 48 8 40

## Trace form

 $$44 q - q^{5} + 16 q^{9} + O(q^{10})$$ $$44 q - q^{5} + 16 q^{9} + 2 q^{11} + 10 q^{15} + 14 q^{19} - 14 q^{21} - 5 q^{25} + 14 q^{31} + 13 q^{35} - 16 q^{39} - 16 q^{41} + 12 q^{45} - 20 q^{49} + 26 q^{51} - 18 q^{55} + 30 q^{59} - 2 q^{61} - 4 q^{65} - 36 q^{69} - 32 q^{71} + 25 q^{75} + 26 q^{79} + 10 q^{81} - 30 q^{85} + 10 q^{89} - 80 q^{91} + 27 q^{95} + 8 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(560, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
560.2.bw.a $4$ $4.472$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$0$$ $$-6$$ $$-2$$ $$-3$$ $$q+(-1-\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{3})q^{5}+\cdots$$
560.2.bw.b $4$ $4.472$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\zeta_{12}q^{3}+(-2\zeta_{12}-\zeta_{12}^{2}+2\zeta_{12}^{3})q^{5}+\cdots$$
560.2.bw.c $4$ $4.472$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+3\zeta_{12}q^{3}+(2\zeta_{12}-\zeta_{12}^{2}-2\zeta_{12}^{3})q^{5}+\cdots$$
560.2.bw.d $4$ $4.472$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(\zeta_{12}+2\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}+(-2\zeta_{12}+\cdots)q^{7}+\cdots$$
560.2.bw.e $4$ $4.472$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$0$$ $$6$$ $$1$$ $$3$$ $$q+(1+\beta _{2})q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+(2\beta _{2}+\cdots)q^{7}+\cdots$$
560.2.bw.f $24$ $4.472$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(560, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(560, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(280, [\chi])$$$$^{\oplus 2}$$