# Properties

 Label 384.2.f Level $384$ Weight $2$ Character orbit 384.f Rep. character $\chi_{384}(191,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $4$ Sturm bound $128$ Trace bound $15$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$384 = 2^{7} \cdot 3$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 384.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$24$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$128$$ Trace bound: $$15$$ Distinguishing $$T_p$$: $$5$$, $$7$$, $$23$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(384, [\chi])$$.

Total New Old
Modular forms 80 16 64
Cusp forms 48 16 32
Eisenstein series 32 0 32

## Trace form

 $$16q + O(q^{10})$$ $$16q + 16q^{25} + 16q^{33} - 48q^{49} + 16q^{57} - 32q^{73} - 48q^{81} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(384, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
384.2.f.a $$4$$ $$3.066$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ $$\Q(\sqrt{-6})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}-3q^{9}-2\beta _{2}q^{11}+\cdots$$
384.2.f.b $$4$$ $$3.066$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{3}+(\zeta_{8}+\zeta_{8}^{2})q^{5}-\zeta_{8}^{3}q^{7}+\cdots$$
384.2.f.c $$4$$ $$3.066$$ $$\Q(\zeta_{8})$$ $$\Q(\sqrt{-2})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{3}+(1-\zeta_{8}^{2})q^{9}+(-2\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots$$
384.2.f.d $$4$$ $$3.066$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{3}+(-\zeta_{8}-\zeta_{8}^{2})q^{5}+\zeta_{8}^{3}q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(384, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(384, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 2}$$