# Properties

 Label 64.9.d Level $64$ Weight $9$ Character orbit 64.d Rep. character $\chi_{64}(31,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $2$ Sturm bound $72$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$64 = 2^{6}$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 64.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$72$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{9}(64, [\chi])$$.

Total New Old
Modular forms 70 16 54
Cusp forms 58 16 42
Eisenstein series 12 0 12

## Trace form

 $$16 q + 34992 q^{9} + O(q^{10})$$ $$16 q + 34992 q^{9} + 231840 q^{17} - 2312432 q^{25} - 4958016 q^{33} + 1691424 q^{41} - 1042416 q^{49} - 24274752 q^{57} - 67850496 q^{65} + 51448480 q^{73} + 392846544 q^{81} + 85417632 q^{89} - 269794912 q^{97} + O(q^{100})$$

## Decomposition of $$S_{9}^{\mathrm{new}}(64, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
64.9.d.a $4$ $26.072$ $$\Q(i, \sqrt{1731})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+\beta _{3}q^{5}-7\beta _{2}q^{7}+363q^{9}+\cdots$$
64.9.d.b $12$ $26.072$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{4}q^{5}+\beta _{10}q^{7}+(2795+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{9}^{\mathrm{old}}(64, [\chi])$$ into lower level spaces

$$S_{9}^{\mathrm{old}}(64, [\chi]) \simeq$$ $$S_{9}^{\mathrm{new}}(8, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 2}$$