# Properties

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

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(64))$$.

Total New Old
Modular forms 14 3 11
Cusp forms 3 1 2
Eisenstein series 11 2 9

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$$2$$Dim
$$-$$$$1$$

## Trace form

 $$q + 2 q^{5} - 3 q^{9} + O(q^{10})$$ $$q + 2 q^{5} - 3 q^{9} - 6 q^{13} + 2 q^{17} - q^{25} + 10 q^{29} + 2 q^{37} + 10 q^{41} - 6 q^{45} - 7 q^{49} - 14 q^{53} + 10 q^{61} - 12 q^{65} - 6 q^{73} + 9 q^{81} + 4 q^{85} + 10 q^{89} + 18 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(64))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
64.2.a.a $1$ $0.511$ $$\Q$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$2$$ $$0$$ $-$ $$q+2q^{5}-3q^{9}-6q^{13}+2q^{17}-q^{25}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(64))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(64)) \simeq$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(32))$$$$^{\oplus 2}$$