# Properties

 Label 384.2.c Level $384$ Weight $2$ Character orbit 384.c Rep. character $\chi_{384}(383,\cdot)$ 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.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$12$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$128$$ Trace bound: $$15$$ Distinguishing $$T_p$$: $$11$$, $$23$$

## 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

 $$16q + O(q^{10})$$ $$16q - 16q^{25} + 16q^{33} + 16q^{49} - 16q^{57} - 32q^{73} + 16q^{81} - 64q^{97} + O(q^{100})$$

## 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.c.a $$4$$ $$3.066$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+(-1+\beta _{3})q^{3}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
384.2.c.b $$4$$ $$3.066$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+(-1+\beta _{3})q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$$
384.2.c.c $$4$$ $$3.066$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+(1+\beta _{1})q^{3}+(\beta _{1}+\beta _{3})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$$
384.2.c.d $$4$$ $$3.066$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+(1+\beta _{1})q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(384, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 2}$$