# Properties

 Label 760.1.bm Level $760$ Weight $1$ Character orbit 760.bm Rep. character $\chi_{760}(539,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $4$ Newform subspaces $2$ Sturm bound $120$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$760 = 2^{3} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 760.bm (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$760$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$120$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(760, [\chi])$$.

Total New Old
Modular forms 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 0

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

 $$4 q - 2 q^{4} - 2 q^{9} + O(q^{10})$$ $$4 q - 2 q^{4} - 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{14} - 2 q^{16} - 2 q^{19} - 2 q^{25} + 8 q^{26} + 2 q^{35} - 2 q^{36} - 2 q^{40} + 2 q^{41} + 2 q^{44} - 4 q^{46} - 4 q^{56} - 4 q^{59} + 4 q^{64} + 8 q^{65} + 2 q^{74} + 4 q^{76} - 2 q^{81} + 2 q^{89} - 2 q^{90} + 4 q^{91} + 8 q^{94} + 2 q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(760, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
760.1.bm.a $2$ $0.379$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-10})$$ None $$-1$$ $$0$$ $$-1$$ $$-2$$ $$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-q^{7}+q^{8}+\cdots$$
760.1.bm.b $2$ $0.379$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-10})$$ None $$1$$ $$0$$ $$1$$ $$2$$ $$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+q^{7}-q^{8}+\cdots$$