# Properties

 Label 855.1.g Level $855$ Weight $1$ Character orbit 855.g Rep. character $\chi_{855}(379,\cdot)$ Character field $\Q$ Dimension $5$ Newform subspaces $3$ Sturm bound $120$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$855 = 3^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 855.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$120$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(855, [\chi])$$.

Total New Old
Modular forms 22 7 15
Cusp forms 14 5 9
Eisenstein series 8 2 6

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 5 0 0 0

## Trace form

 $$5 q - q^{4} + q^{5} + O(q^{10})$$ $$5 q - q^{4} + q^{5} + 2 q^{11} + q^{16} - 3 q^{19} + 3 q^{20} + q^{25} - 4 q^{26} - 2 q^{44} + 5 q^{49} - 2 q^{55} + 2 q^{61} - 5 q^{64} + 4 q^{74} - q^{76} - 3 q^{80} - 4 q^{85} - 3 q^{95} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(855, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
855.1.g.a $1$ $0.427$ $$\Q$$ $D_{2}$ $$\Q(\sqrt{-19})$$, $$\Q(\sqrt{-95})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$-1$$ $$0$$ $$q-q^{4}-q^{5}+2q^{11}+q^{16}+q^{19}+\cdots$$
855.1.g.b $2$ $0.427$ $$\Q(\sqrt{-1})$$ $D_{2}$ $$\Q(\sqrt{-15})$$, $$\Q(\sqrt{-19})$$ $$\Q(\sqrt{285})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-q^{4}-iq^{5}+q^{16}-iq^{17}-q^{19}+\cdots$$
855.1.g.c $2$ $0.427$ $$\Q(\sqrt{2})$$ $D_{4}$ $$\Q(\sqrt{-95})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\beta q^{2}+q^{4}+q^{5}-\beta q^{10}+\beta q^{13}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(855, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(855, [\chi]) \simeq$$ $$S_{1}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(285, [\chi])$$$$^{\oplus 2}$$