# Properties

 Label 3724.1.e Level $3724$ Weight $1$ Character orbit 3724.e Rep. character $\chi_{3724}(1177,\cdot)$ Character field $\Q$ Dimension $5$ Newform subspaces $5$ 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.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q$$ Newform subspaces: $$5$$ 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 38 5 33
Cusp forms 14 5 9
Eisenstein series 24 0 24

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 5 0 0 0

## Trace form

 $$5q + q^{5} + 5q^{9} + O(q^{10})$$ $$5q + q^{5} + 5q^{9} + q^{11} + q^{17} - q^{19} - 2q^{23} + 6q^{25} + q^{43} + q^{45} + q^{47} - q^{55} + q^{61} + q^{73} + 5q^{81} - 2q^{83} - q^{85} + q^{95} + q^{99} + O(q^{100})$$

## 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.e.a $$1$$ $$1.859$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-2q^{5}+q^{9}-q^{11}+q^{17}-q^{19}+\cdots$$
3724.1.e.b $$1$$ $$1.859$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-1$$ $$0$$ $$q-q^{5}+q^{9}+2q^{11}-q^{17}+q^{19}+\cdots$$
3724.1.e.c $$1$$ $$1.859$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$1$$ $$0$$ $$q+q^{5}+q^{9}-q^{11}+q^{17}-q^{19}+2q^{23}+\cdots$$
3724.1.e.d $$1$$ $$1.859$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$1$$ $$0$$ $$q+q^{5}+q^{9}+2q^{11}+q^{17}-q^{19}+\cdots$$
3724.1.e.e $$1$$ $$1.859$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+2q^{5}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots$$

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

$$S_{1}^{\mathrm{old}}(3724, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(76, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(931, [\chi])$$$$^{\oplus 3}$$