# Properties

 Label 384.1.h Level $384$ Weight $1$ Character orbit 384.h Rep. character $\chi_{384}(65,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $2$ Sturm bound $64$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$384 = 2^{7} \cdot 3$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 384.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$24$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$64$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(384, [\chi])$$.

Total New Old
Modular forms 22 2 20
Cusp forms 6 2 4
Eisenstein series 16 0 16

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

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

## Trace form

 $$2q + 2q^{9} + O(q^{10})$$ $$2q + 2q^{9} - 2q^{25} - 4q^{33} - 2q^{49} - 4q^{73} + 2q^{81} + 4q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(384, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
384.1.h.a $$1$$ $$0.192$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-2})$$, $$\Q(\sqrt{-6})$$ $$\Q(\sqrt{3})$$ $$0$$ $$-1$$ $$0$$ $$0$$ $$q-q^{3}+q^{9}+2q^{11}-q^{25}-q^{27}+\cdots$$
384.1.h.b $$1$$ $$0.192$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-2})$$, $$\Q(\sqrt{-6})$$ $$\Q(\sqrt{3})$$ $$0$$ $$1$$ $$0$$ $$0$$ $$q+q^{3}+q^{9}-2q^{11}-q^{25}+q^{27}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(384, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(384, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 2}$$