# Properties

 Label 384.2.j Level $384$ Weight $2$ Character orbit 384.j Rep. character $\chi_{384}(97,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $16$ Newform subspaces $2$ Sturm bound $128$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$384 = 2^{7} \cdot 3$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 384.j (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$16$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$128$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$11$$

## Dimensions

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

Total New Old
Modular forms 160 16 144
Cusp forms 96 16 80
Eisenstein series 64 0 64

## Trace form

 $$16 q + O(q^{10})$$ $$16 q + 32 q^{29} + 32 q^{37} - 16 q^{49} - 32 q^{53} - 32 q^{61} - 32 q^{65} - 32 q^{69} - 32 q^{77} - 16 q^{81} + 32 q^{85} + O(q^{100})$$

## 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.j.a $8$ $3.066$ 8.0.18939904.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+(\beta _{3}-\beta _{5})q^{5}+(\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{7}+\cdots$$
384.2.j.b $8$ $3.066$ 8.0.18939904.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}+(-\beta _{2}+\beta _{6})q^{5}+(\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(384, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(128, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 2}$$