# Properties

 Label 560.2.g Level $560$ Weight $2$ Character orbit 560.g Rep. character $\chi_{560}(449,\cdot)$ Character field $\Q$ Dimension $18$ 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.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$192$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$, $$11$$

## Dimensions

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

Total New Old
Modular forms 108 18 90
Cusp forms 84 18 66
Eisenstein series 24 0 24

## Trace form

 $$18 q + 2 q^{5} - 18 q^{9} + O(q^{10})$$ $$18 q + 2 q^{5} - 18 q^{9} - 12 q^{11} + 12 q^{15} + 8 q^{19} + 2 q^{25} - 4 q^{29} - 8 q^{31} - 28 q^{39} - 4 q^{41} - 10 q^{45} - 18 q^{49} - 20 q^{51} + 40 q^{55} + 36 q^{61} - 16 q^{65} - 16 q^{69} + 40 q^{71} - 12 q^{79} + 34 q^{81} + 20 q^{89} - 12 q^{91} + 32 q^{95} + 56 q^{99} + O(q^{100})$$

## 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.g.a $2$ $4.472$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+3iq^{3}+(-2-i)q^{5}-iq^{7}-6q^{9}+\cdots$$
560.2.g.b $2$ $4.472$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+iq^{3}+(-2-i)q^{5}+iq^{7}+2q^{9}+\cdots$$
560.2.g.c $2$ $4.472$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1+2i)q^{5}-iq^{7}+3q^{9}-4iq^{13}+\cdots$$
560.2.g.d $2$ $4.472$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+iq^{3}+(2+i)q^{5}+iq^{7}+2q^{9}+q^{11}+\cdots$$
560.2.g.e $4$ $4.472$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(\beta _{1}+\beta _{3})q^{3}+(1+\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+\cdots$$
560.2.g.f $6$ $4.472$ 6.0.5161984.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{3}+(\beta _{2}+\beta _{5})q^{5}+\beta _{4}q^{7}+(-1+\cdots)q^{9}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(560, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(280, [\chi])$$$$^{\oplus 2}$$