# Properties

 Label 1944.1.e Level $1944$ Weight $1$ Character orbit 1944.e Rep. character $\chi_{1944}(1457,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $324$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1944 = 2^{3} \cdot 3^{5}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1944.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$324$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1944, [\chi])$$.

Total New Old
Modular forms 52 2 50
Cusp forms 16 2 14
Eisenstein series 36 0 36

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 0 0 2 0

## Trace form

 $$2 q + O(q^{10})$$ $$2 q + 2 q^{13} - 2 q^{19} - 2 q^{25} - 2 q^{31} + 2 q^{43} - 2 q^{49} - 4 q^{55} + 2 q^{61} - 2 q^{67} + 2 q^{73} + 2 q^{79} + 4 q^{85} - 2 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1944, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1944.1.e.a $$2$$ $$0.970$$ $$\Q(\sqrt{-2})$$ $$S_{4}$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta q^{5}-\beta q^{11}+q^{13}+\beta q^{17}-q^{19}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(1944, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(1944, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(108, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(243, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(972, [\chi])$$$$^{\oplus 2}$$