# Properties

 Label 1944.1.h Level $1944$ Weight $1$ Character orbit 1944.h Rep. character $\chi_{1944}(485,\cdot)$ Character field $\Q$ Dimension $10$ Newform subspaces $3$ Sturm bound $324$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1944 = 2^{3} \cdot 3^{5}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1944.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$24$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$324$$ Trace bound: $$2$$

## Dimensions

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

Total New Old
Modular forms 34 10 24
Cusp forms 16 10 6
Eisenstein series 18 0 18

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 6 0 4 0

## Trace form

 $$10 q + 6 q^{4} + 4 q^{7} + O(q^{10})$$ $$10 q + 6 q^{4} + 4 q^{7} - 4 q^{10} + 2 q^{16} + 10 q^{25} - 4 q^{31} - 4 q^{34} + 4 q^{40} - 4 q^{46} + 6 q^{49} - 4 q^{52} - 6 q^{55} - 6 q^{58} + 6 q^{64} - 10 q^{70} + 4 q^{76} - 2 q^{79} + 4 q^{82} + 4 q^{97} + O(q^{100})$$

## 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.h.a $$3$$ $$0.970$$ $$\Q(\zeta_{18})^+$$ $$D_{9}$$ $$\Q(\sqrt{-6})$$ None $$-3$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+q^{4}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots$$
1944.1.h.b $$3$$ $$0.970$$ $$\Q(\zeta_{18})^+$$ $$D_{9}$$ $$\Q(\sqrt{-6})$$ None $$3$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+q^{4}-\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots$$
1944.1.h.c $$4$$ $$0.970$$ $$\Q(\zeta_{8})$$ $$S_{4}$$ None None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$$

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

$$S_{1}^{\mathrm{old}}(1944, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(216, [\chi])$$$$^{\oplus 3}$$