# Properties

 Label 740.1.g Level $740$ Weight $1$ Character orbit 740.g Rep. character $\chi_{740}(739,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $4$ Sturm bound $114$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$740 = 2^{2} \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 740.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$740$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$114$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(740, [\chi])$$.

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

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

 $$6 q + 6 q^{4} + 2 q^{9} + O(q^{10})$$ $$6 q + 6 q^{4} + 2 q^{9} - 2 q^{10} + 6 q^{16} - 8 q^{21} + 6 q^{25} - 4 q^{26} - 4 q^{34} + 2 q^{36} - 2 q^{40} - 4 q^{41} + 2 q^{49} + 6 q^{64} - 4 q^{65} - 2 q^{74} - 2 q^{81} - 8 q^{84} - 4 q^{85} - 6 q^{90} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(740, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
740.1.g.a $1$ $0.369$ $$\Q$$ $D_{2}$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-185})$$ $$\Q(\sqrt{185})$$ $$-1$$ $$0$$ $$-1$$ $$0$$ $$q-q^{2}+q^{4}-q^{5}-q^{8}-q^{9}+q^{10}+\cdots$$
740.1.g.b $1$ $0.369$ $$\Q$$ $D_{2}$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-185})$$ $$\Q(\sqrt{185})$$ $$1$$ $$0$$ $$1$$ $$0$$ $$q+q^{2}+q^{4}+q^{5}+q^{8}-q^{9}+q^{10}+\cdots$$
740.1.g.c $2$ $0.369$ $$\Q(\sqrt{2})$$ $D_{4}$ $$\Q(\sqrt{-185})$$ None $$-2$$ $$0$$ $$2$$ $$0$$ $$q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+\beta q^{7}+\cdots$$
740.1.g.d $2$ $0.369$ $$\Q(\sqrt{2})$$ $D_{4}$ $$\Q(\sqrt{-185})$$ None $$2$$ $$0$$ $$-2$$ $$0$$ $$q+q^{2}-\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+\beta q^{7}+\cdots$$