# Properties

 Label 384.5.b Level $384$ Weight $5$ Character orbit 384.b Rep. character $\chi_{384}(319,\cdot)$ Character field $\Q$ Dimension $32$ Newform subspaces $4$ Sturm bound $320$ Trace bound $17$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$384 = 2^{7} \cdot 3$$ Weight: $$k$$ $$=$$ $$5$$ Character orbit: $$[\chi]$$ $$=$$ 384.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$320$$ Trace bound: $$17$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(384, [\chi])$$.

Total New Old
Modular forms 272 32 240
Cusp forms 240 32 208
Eisenstein series 32 0 32

## Trace form

 $$32 q + 864 q^{9} + O(q^{10})$$ $$32 q + 864 q^{9} + 960 q^{17} - 2656 q^{25} + 2880 q^{41} - 16992 q^{49} - 14976 q^{57} + 26880 q^{65} + 46400 q^{73} + 23328 q^{81} - 37440 q^{89} - 50496 q^{97} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(384, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
384.5.b.a $4$ $39.694$ $$\Q(\sqrt{3}, \sqrt{-19})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3\beta _{1}q^{3}+\beta _{2}q^{5}+\beta _{3}q^{7}+3^{3}q^{9}+\cdots$$
384.5.b.b $4$ $39.694$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+3^{3}q^{9}+\cdots$$
384.5.b.c $8$ $39.694$ 8.0.49787136.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+(\beta _{1}-\beta _{3})q^{5}-\beta _{5}q^{7}+3^{3}q^{9}+\cdots$$
384.5.b.d $16$ $39.694$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}+\beta _{11}q^{5}-\beta _{5}q^{7}+3^{3}q^{9}+\cdots$$

## Decomposition of $$S_{5}^{\mathrm{old}}(384, [\chi])$$ into lower level spaces

$$S_{5}^{\mathrm{old}}(384, [\chi]) \cong$$ $$S_{5}^{\mathrm{new}}(8, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(128, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 2}$$