# Properties

 Label 740.1.bj Level $740$ Weight $1$ Character orbit 740.bj Rep. character $\chi_{740}(103,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $4$ Newform subspaces $1$ Sturm bound $114$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$740 = 2^{2} \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 740.bj (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$740$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$1$$ Sturm bound: $$114$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 20 20 0
Cusp forms 4 4 0
Eisenstein series 16 16 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

 $$4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{8} + O(q^{10})$$ $$4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{8} - 2 q^{10} - 2 q^{16} - 4 q^{20} - 2 q^{25} - 2 q^{29} + 2 q^{32} + 2 q^{37} - 2 q^{40} + 6 q^{41} - 4 q^{50} - 2 q^{53} + 2 q^{58} - 4 q^{61} + 4 q^{64} + 4 q^{73} + 4 q^{74} + 2 q^{80} + 2 q^{81} + 2 q^{89} + O(q^{100})$$

## 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.bj.a $4$ $0.369$ $$\Q(\zeta_{12})$$ $D_{12}$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$2$$ $$0$$ $$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{5}+\cdots$$