# Properties

 Label 1340.1.bl Level $1340$ Weight $1$ Character orbit 1340.bl Rep. character $\chi_{1340}(19,\cdot)$ Character field $\Q(\zeta_{66})$ Dimension $40$ Newform subspaces $2$ Sturm bound $204$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1340 = 2^{2} \cdot 5 \cdot 67$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1340.bl (of order $$66$$ and degree $$20$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1340$$ Character field: $$\Q(\zeta_{66})$$ Newform subspaces: $$2$$ Sturm bound: $$204$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1340, [\chi])$$.

Total New Old
Modular forms 120 120 0
Cusp forms 40 40 0
Eisenstein series 80 80 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 40 0 0 0

## Trace form

 $$40q + 2q^{4} - 4q^{5} - 2q^{6} + O(q^{10})$$ $$40q + 2q^{4} - 4q^{5} - 2q^{6} + 4q^{14} + 2q^{16} + 2q^{20} - 20q^{21} - 18q^{24} - 4q^{25} - 2q^{29} - 2q^{30} - 2q^{41} - 2q^{46} + 2q^{54} - 2q^{56} - 18q^{61} - 4q^{64} + 2q^{69} - 18q^{70} + 2q^{80} + 4q^{81} + 2q^{84} - 2q^{86} - 8q^{89} + 4q^{94} - 2q^{96} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1340, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1340.1.bl.a $$20$$ $$0.669$$ $$\Q(\zeta_{33})$$ $$D_{33}$$ $$\Q(\sqrt{-5})$$ None $$-1$$ $$-2$$ $$-2$$ $$1$$ $$q+\zeta_{66}^{31}q^{2}+(\zeta_{66}^{17}+\zeta_{66}^{25})q^{3}+\cdots$$
1340.1.bl.b $$20$$ $$0.669$$ $$\Q(\zeta_{33})$$ $$D_{33}$$ $$\Q(\sqrt{-5})$$ None $$1$$ $$2$$ $$-2$$ $$-1$$ $$q-\zeta_{66}^{31}q^{2}+(-\zeta_{66}^{17}-\zeta_{66}^{25}+\cdots)q^{3}+\cdots$$