# Properties

 Label 260.1.s Level $260$ Weight $1$ Character orbit 260.s Rep. character $\chi_{260}(187,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $2$ Newform subspaces $1$ Sturm bound $42$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$260 = 2^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 260.s (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$260$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$42$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(260, [\chi])$$.

Total New Old
Modular forms 10 10 0
Cusp forms 2 2 0
Eisenstein series 8 8 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 0 0

## Trace form

 $$2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + O(q^{10})$$ $$2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + 2 q^{16} + 2 q^{17} - 2 q^{25} - 2 q^{32} - 2 q^{34} - 2 q^{41} - 2 q^{45} - 2 q^{49} + 2 q^{50} - 2 q^{53} + 2 q^{64} + 2 q^{65} + 2 q^{68} + 4 q^{73} - 2 q^{81} + 2 q^{82} - 2 q^{85} + 2 q^{89} + 2 q^{90} + 2 q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(260, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
260.1.s.a $2$ $0.130$ $$\Q(\sqrt{-1})$$ $D_{4}$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+q^{4}+iq^{5}-q^{8}+iq^{9}-iq^{10}+\cdots$$