# Properties

 Label 1560.1.cs Level $1560$ Weight $1$ Character orbit 1560.cs Rep. character $\chi_{1560}(467,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $40$ Newform subspaces $6$ Sturm bound $336$ Trace bound $10$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1560.cs (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1560$$ Character field: $$\Q(i)$$ Newform subspaces: $$6$$ Sturm bound: $$336$$ Trace bound: $$10$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1560, [\chi])$$.

Total New Old
Modular forms 56 56 0
Cusp forms 40 40 0
Eisenstein series 16 16 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 40 0 0 0

## Trace form

 $$40 q + O(q^{10})$$ $$40 q + 8 q^{10} - 8 q^{12} - 24 q^{16} - 8 q^{22} + 12 q^{27} - 4 q^{30} + 8 q^{40} - 12 q^{42} - 16 q^{43} + 8 q^{52} + 12 q^{75} - 16 q^{81} - 8 q^{82} - 8 q^{88} + 12 q^{90} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1560, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1560.1.cs.a $4$ $0.779$ $$\Q(\zeta_{8})$$ $D_{4}$ $$\Q(\sqrt{-26})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\cdots$$
1560.1.cs.b $4$ $0.779$ $$\Q(\zeta_{8})$$ $D_{4}$ $$\Q(\sqrt{-26})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{2}+q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\cdots$$
1560.1.cs.c $8$ $0.779$ $$\Q(\zeta_{24})$$ $D_{12}$ $$\Q(\sqrt{-26})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+\zeta_{24}^{9}q^{2}+\zeta_{24}^{8}q^{3}-\zeta_{24}^{6}q^{4}+\cdots$$
1560.1.cs.d $8$ $0.779$ $$\Q(\zeta_{16})$$ $D_{8}$ $$\Q(\sqrt{-39})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{3}-\zeta_{16}^{2}q^{4}+\cdots$$
1560.1.cs.e $8$ $0.779$ $$\Q(\zeta_{16})$$ $D_{8}$ $$\Q(\sqrt{-39})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{2}q^{3}+\zeta_{16}^{6}q^{4}+\cdots$$
1560.1.cs.f $8$ $0.779$ $$\Q(\zeta_{24})$$ $D_{12}$ $$\Q(\sqrt{-26})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{9}q^{2}+\zeta_{24}^{2}q^{3}-\zeta_{24}^{6}q^{4}+\cdots$$