# Properties

 Label 1805.1.o Level $1805$ Weight $1$ Character orbit 1805.o Rep. character $\chi_{1805}(299,\cdot)$ Character field $\Q(\zeta_{18})$ Dimension $18$ Newform subspaces $2$ Sturm bound $190$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1805 = 5 \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1805.o (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q(\zeta_{18})$$ Newform subspaces: $$2$$ Sturm bound: $$190$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1805, [\chi])$$.

Total New Old
Modular forms 138 114 24
Cusp forms 18 18 0
Eisenstein series 120 96 24

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 18 0 0 0

## Trace form

 $$18 q + O(q^{10})$$ $$18 q + 6 q^{11} - 18 q^{20} - 12 q^{26} - 12 q^{30} - 24 q^{39} + 9 q^{45} - 9 q^{49} + 9 q^{64} + 24 q^{96} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1805, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1805.1.o.a $6$ $0.901$ $$\Q(\zeta_{18})$$ $D_{2}$ $$\Q(\sqrt{-19})$$, $$\Q(\sqrt{-95})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{18}^{2}q^{4}-\zeta_{18}^{7}q^{5}-\zeta_{18}^{8}q^{9}+\cdots$$
1805.1.o.b $12$ $0.901$ 12.0.$$\cdots$$.2 $D_{4}$ $$\Q(\sqrt{-95})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{5}+\beta _{11})q^{2}+\beta _{5}q^{3}+(-\beta _{4}-\beta _{10}+\cdots)q^{4}+\cdots$$