# Properties

 Label 384.2.d Level $384$ Weight $2$ Character orbit 384.d Rep. character $\chi_{384}(193,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $3$ Sturm bound $128$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$384 = 2^{7} \cdot 3$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 384.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$128$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

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

Total New Old
Modular forms 80 8 72
Cusp forms 48 8 40
Eisenstein series 32 0 32

## Trace form

 $$8q - 8q^{9} + O(q^{10})$$ $$8q - 8q^{9} - 16q^{17} + 8q^{25} + 16q^{41} + 40q^{49} - 32q^{57} - 64q^{65} + 16q^{73} + 8q^{81} + 48q^{89} + 48q^{97} + O(q^{100})$$

## 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.d.a $$2$$ $$3.066$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+iq^{3}-4q^{7}-q^{9}+4iq^{11}+4iq^{13}+\cdots$$
384.2.d.b $$2$$ $$3.066$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q+iq^{3}+4q^{7}-q^{9}+4iq^{11}-4iq^{13}+\cdots$$
384.2.d.c $$4$$ $$3.066$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}+\zeta_{8}^{3}q^{7}-q^{9}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(384, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(128, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 2}$$