# Properties

 Label 3724.1.dj Level $3724$ Weight $1$ Character orbit 3724.dj Rep. character $\chi_{3724}(37,\cdot)$ Character field $\Q(\zeta_{42})$ Dimension $24$ Newform subspaces $2$ Sturm bound $560$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3724 = 2^{2} \cdot 7^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3724.dj (of order $$42$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$931$$ Character field: $$\Q(\zeta_{42})$$ Newform subspaces: $$2$$ Sturm bound: $$560$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(3724, [\chi])$$.

Total New Old
Modular forms 132 24 108
Cusp forms 60 24 36
Eisenstein series 72 0 72

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 24 0 0 0

## Trace form

 $$24q + q^{5} - q^{7} + 2q^{9} + O(q^{10})$$ $$24q + q^{5} - q^{7} + 2q^{9} + 8q^{11} + 5q^{17} - 12q^{19} - 2q^{23} + 3q^{25} - 5q^{35} - 2q^{43} - 13q^{45} + q^{47} - q^{49} - 6q^{55} + q^{61} - q^{63} + q^{73} + q^{77} + 2q^{81} + 4q^{83} + 2q^{85} + q^{95} - 2q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(3724, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
3724.1.dj.a $$12$$ $$1.859$$ $$\Q(\zeta_{21})$$ $$D_{21}$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-1$$ $$-2$$ $$q+(-\zeta_{42}-\zeta_{42}^{3})q^{5}-\zeta_{42}^{9}q^{7}-\zeta_{42}^{11}q^{9}+\cdots$$
3724.1.dj.b $$12$$ $$1.859$$ $$\Q(\zeta_{21})$$ $$D_{21}$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$2$$ $$1$$ $$q+(\zeta_{42}^{8}-\zeta_{42}^{17})q^{5}+\zeta_{42}^{16}q^{7}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(3724, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(3724, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(931, [\chi])$$$$^{\oplus 3}$$