# Properties

 Label 1805.1.h Level $1805$ Weight $1$ Character orbit 1805.h Rep. character $\chi_{1805}(69,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $6$ 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.h (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q(\zeta_{6})$$ 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 46 38 8
Cusp forms 6 6 0
Eisenstein series 40 32 8

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 6 0 0 0

## Trace form

 $$6 q - q^{4} + q^{5} + 4 q^{6} - q^{9} + O(q^{10})$$ $$6 q - q^{4} + q^{5} + 4 q^{6} - q^{9} - 4 q^{11} + q^{16} - 6 q^{20} - 3 q^{25} + 8 q^{26} + 8 q^{30} - 3 q^{36} - 8 q^{39} - 2 q^{44} - 6 q^{45} + 6 q^{49} + 2 q^{55} + 2 q^{61} - 6 q^{64} + 4 q^{74} - 3 q^{80} + q^{81} + 8 q^{96} - 2 q^{99} + O(q^{100})$$

## 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.h.a $2$ $0.901$ $$\Q(\sqrt{-3})$$ $D_{2}$ $$\Q(\sqrt{-19})$$, $$\Q(\sqrt{-95})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$-1$$ $$0$$ $$q+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{9}-q^{11}+\cdots$$
1805.1.h.b $4$ $0.901$ $$\Q(\sqrt{2}, \sqrt{-3})$$ $D_{4}$ $$\Q(\sqrt{-95})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$$