# Properties

 Label 775.1.z Level $775$ Weight $1$ Character orbit 775.z Rep. character $\chi_{775}(154,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $12$ Newform subspaces $2$ Sturm bound $80$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$775 = 5^{2} \cdot 31$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 775.z (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$775$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$2$$ Sturm bound: $$80$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(775, [\chi])$$.

Total New Old
Modular forms 20 20 0
Cusp forms 12 12 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 12 0 0 0

## Trace form

 $$12 q + 3 q^{4} - 15 q^{8} + 3 q^{9} + O(q^{10})$$ $$12 q + 3 q^{4} - 15 q^{8} + 3 q^{9} + 3 q^{10} - 6 q^{14} - 3 q^{16} + 3 q^{20} + 3 q^{31} - 3 q^{35} - 3 q^{36} + 15 q^{38} - 3 q^{40} - 12 q^{49} + 3 q^{50} - 9 q^{56} + 12 q^{64} - 15 q^{67} - 3 q^{70} - 15 q^{72} + 6 q^{76} - 3 q^{81} + 12 q^{90} - 3 q^{95} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(775, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
775.1.z.a $4$ $0.387$ $$\Q(\zeta_{10})$$ $D_{10}$ $$\Q(\sqrt{-31})$$ None $$-5$$ $$0$$ $$1$$ $$0$$ $$q+(-1+\zeta_{10}^{4})q^{2}+(1-\zeta_{10}^{3}-\zeta_{10}^{4}+\cdots)q^{4}+\cdots$$
775.1.z.b $8$ $0.387$ $$\Q(\zeta_{15})$$ $D_{30}$ $$\Q(\sqrt{-31})$$ None $$5$$ $$0$$ $$-1$$ $$0$$ $$q+(\zeta_{30}^{2}-\zeta_{30}^{10})q^{2}+(\zeta_{30}^{4}-\zeta_{30}^{5}+\cdots)q^{4}+\cdots$$