# Properties

 Label 3724.1.bc Level $3724$ Weight $1$ Character orbit 3724.bc Rep. character $\chi_{3724}(569,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $8$ Newform subspaces $4$ Sturm bound $560$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3724 = 2^{2} \cdot 7^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3724.bc (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$133$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$560$$ Trace bound: $$11$$

## Dimensions

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

Total New Old
Modular forms 82 8 74
Cusp forms 34 8 26
Eisenstein series 48 0 48

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 8 0 0 0

## Trace form

 $$8q + q^{5} - 4q^{9} + O(q^{10})$$ $$8q + q^{5} - 4q^{9} + q^{11} - 2q^{17} + 2q^{19} - 2q^{23} - 3q^{25} - 2q^{43} + q^{45} + q^{47} + 8q^{55} + q^{61} + q^{73} - 4q^{81} + 4q^{83} + 2q^{85} + q^{95} - 2q^{99} + O(q^{100})$$

## 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.bc.a $$2$$ $$1.859$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-1$$ $$0$$ $$q-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\zeta_{6}^{2}q^{11}+\zeta_{6}^{2}q^{17}+\cdots$$
3724.1.bc.b $$2$$ $$1.859$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-1$$ $$0$$ $$q-\zeta_{6}q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\zeta_{6}^{2}q^{17}+\cdots$$
3724.1.bc.c $$2$$ $$1.859$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$1$$ $$0$$ $$q+\zeta_{6}q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}-\zeta_{6}^{2}q^{17}+\cdots$$
3724.1.bc.d $$2$$ $$1.859$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\zeta_{6}q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\zeta_{6}^{2}q^{17}+\cdots$$

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

$$S_{1}^{\mathrm{old}}(3724, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(133, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(532, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(931, [\chi])$$$$^{\oplus 3}$$