# Properties

 Label 775.1.d Level $775$ Weight $1$ Character orbit 775.d Rep. character $\chi_{775}(526,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $3$ Sturm bound $80$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$775 = 5^{2} \cdot 31$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 775.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$31$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$80$$ Trace bound: $$2$$

## Dimensions

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

Total New Old
Modular forms 13 7 6
Cusp forms 7 4 3
Eisenstein series 6 3 3

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 4 0 0 0

## Trace form

 $$4 q + q^{2} + 3 q^{4} + q^{7} - q^{8} + 4 q^{9} + O(q^{10})$$ $$4 q + q^{2} + 3 q^{4} + q^{7} - q^{8} + 4 q^{9} - 5 q^{14} + 2 q^{16} + q^{18} - q^{19} - 2 q^{31} + 3 q^{36} - q^{38} - q^{41} - 2 q^{47} + 3 q^{49} - 7 q^{56} - q^{59} + q^{62} + q^{63} - 2 q^{64} - 2 q^{67} - q^{71} - q^{72} - 6 q^{76} + 4 q^{81} - q^{82} - 2 q^{94} + q^{97} + O(q^{100})$$

## 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.d.a $$1$$ $$0.387$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-31})$$, $$\Q(\sqrt{-155})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-q^{4}+q^{9}+q^{16}+2q^{19}-q^{31}+\cdots$$
775.1.d.b $$1$$ $$0.387$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-31})$$ None $$1$$ $$0$$ $$0$$ $$1$$ $$q+q^{2}+q^{7}-q^{8}+q^{9}+q^{14}-q^{16}+\cdots$$
775.1.d.c $$2$$ $$0.387$$ $$\Q(\sqrt{3})$$ $$D_{6}$$ $$\Q(\sqrt{-31})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta q^{2}+2q^{4}+\beta q^{7}-\beta q^{8}+q^{9}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(775, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(775, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(31, [\chi])$$$$^{\oplus 3}$$