# Properties

 Label 560.2.q Level $560$ Weight $2$ Character orbit 560.q Rep. character $\chi_{560}(81,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $32$ Newform subspaces $12$ Sturm bound $192$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$560 = 2^{4} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 560.q (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$12$$ Sturm bound: $$192$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$, $$11$$, $$13$$

## Dimensions

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

Total New Old
Modular forms 216 32 184
Cusp forms 168 32 136
Eisenstein series 48 0 48

## Trace form

 $$32 q - 4 q^{3} - 4 q^{7} - 16 q^{9} + O(q^{10})$$ $$32 q - 4 q^{3} - 4 q^{7} - 16 q^{9} + 4 q^{11} + 4 q^{19} + 4 q^{21} + 4 q^{23} - 16 q^{25} + 32 q^{27} + 24 q^{29} + 16 q^{31} - 8 q^{37} - 8 q^{39} + 8 q^{41} - 40 q^{43} - 4 q^{45} + 20 q^{47} - 16 q^{49} - 32 q^{51} - 16 q^{53} - 16 q^{55} - 16 q^{57} - 8 q^{59} - 8 q^{61} - 56 q^{63} - 4 q^{65} + 24 q^{67} + 16 q^{69} + 32 q^{71} + 8 q^{73} - 4 q^{75} - 24 q^{77} + 24 q^{79} - 12 q^{81} + 112 q^{83} + 60 q^{87} + 12 q^{89} + 24 q^{91} - 16 q^{93} + 32 q^{97} - 88 q^{99} + O(q^{100})$$

## 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.q.a $2$ $4.472$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$1$$ $$-1$$ $$q+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots$$
560.2.q.b $2$ $4.472$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$-1$$ $$4$$ $$q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$$
560.2.q.c $2$ $4.472$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$1$$ $$-4$$ $$q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$$
560.2.q.d $2$ $4.472$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$1$$ $$4$$ $$q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots$$
560.2.q.e $2$ $4.472$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$1$$ $$-1$$ $$q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots$$
560.2.q.f $2$ $4.472$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$1$$ $$-5$$ $$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots$$
560.2.q.g $2$ $4.472$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$1$$ $$1$$ $$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots$$
560.2.q.h $2$ $4.472$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$1$$ $$5$$ $$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots$$
560.2.q.i $2$ $4.472$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$1$$ $$-1$$ $$q+(3-3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots$$
560.2.q.j $4$ $4.472$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$-2$$ $$-2$$ $$2$$ $$q+(-1+\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$$
560.2.q.k $4$ $4.472$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$2$$ $$-2$$ $$-2$$ $$q+(1+\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$$
560.2.q.l $6$ $4.472$ 6.0.11337408.1 None $$0$$ $$0$$ $$-3$$ $$-6$$ $$q+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}-\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(560, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(112, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(280, [\chi])$$$$^{\oplus 2}$$