# Properties

 Label 64.2.e Level $64$ Weight $2$ Character orbit 64.e Rep. character $\chi_{64}(17,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $2$ Newform subspaces $1$ Sturm bound $16$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$64 = 2^{6}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 64.e (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$16$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$16$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(64, [\chi])$$.

Total New Old
Modular forms 24 6 18
Cusp forms 8 2 6
Eisenstein series 16 4 12

## Trace form

 $$2 q + 2 q^{3} - 2 q^{5} + O(q^{10})$$ $$2 q + 2 q^{3} - 2 q^{5} - 2 q^{11} - 2 q^{13} - 4 q^{15} - 4 q^{17} - 6 q^{19} + 4 q^{21} + 8 q^{27} + 6 q^{29} + 16 q^{31} - 4 q^{33} + 4 q^{35} + 6 q^{37} - 10 q^{43} + 2 q^{45} - 16 q^{47} + 6 q^{49} - 4 q^{51} - 10 q^{53} + 6 q^{59} - 18 q^{61} - 4 q^{63} + 4 q^{65} + 10 q^{67} - 12 q^{69} - 6 q^{75} + 4 q^{77} + 10 q^{81} + 2 q^{83} + 4 q^{85} - 4 q^{91} + 16 q^{93} + 12 q^{95} - 4 q^{97} + 2 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(64, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
64.2.e.a $2$ $0.511$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$-2$$ $$0$$ $$q+(1-i)q^{3}+(-1-i)q^{5}+2iq^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(64, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(64, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 3}$$