# Properties

 Label 64.8.b Level $64$ Weight $8$ Character orbit 64.b Rep. character $\chi_{64}(33,\cdot)$ Character field $\Q$ Dimension $14$ Newform subspaces $3$ Sturm bound $64$ Trace bound $1$

# Related objects

## Defining parameters

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

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(64, [\chi])$$.

Total New Old
Modular forms 62 14 48
Cusp forms 50 14 36
Eisenstein series 12 0 12

## Trace form

 $$14 q - 10206 q^{9} + O(q^{10})$$ $$14 q - 10206 q^{9} - 8724 q^{17} - 170378 q^{25} - 297048 q^{33} - 3127476 q^{41} + 2669182 q^{49} + 5161224 q^{57} + 999936 q^{65} - 1493828 q^{73} + 5427462 q^{81} + 15671772 q^{89} - 23867380 q^{97} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(64, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
64.8.b.a $2$ $19.993$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-2})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+43iq^{3}-5209q^{9}+4407iq^{11}+\cdots$$
64.8.b.b $4$ $19.993$ $$\Q(i, \sqrt{435})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+15\beta _{1}q^{3}+\beta _{3}q^{5}+\beta _{2}q^{7}+1287q^{9}+\cdots$$
64.8.b.c $8$ $19.993$ 8.0.$$\cdots$$.10 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{4}+\beta _{6})q^{3}+\beta _{1}q^{5}-\beta _{7}q^{7}+(-617+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{8}^{\mathrm{old}}(64, [\chi])$$ into lower level spaces

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