# Properties

 Label 64.3.f Level $64$ Weight $3$ Character orbit 64.f Rep. character $\chi_{64}(15,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $6$ Newform subspaces $1$ Sturm bound $24$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$64 = 2^{6}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 64.f (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$16$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$24$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(64, [\chi])$$.

Total New Old
Modular forms 40 10 30
Cusp forms 24 6 18
Eisenstein series 16 4 12

## Trace form

 $$6q + 2q^{3} - 2q^{5} + 4q^{7} + O(q^{10})$$ $$6q + 2q^{3} - 2q^{5} + 4q^{7} + 18q^{11} - 2q^{13} - 4q^{17} - 30q^{19} - 20q^{21} - 60q^{23} - 64q^{27} - 18q^{29} - 4q^{33} + 100q^{35} + 46q^{37} + 196q^{39} + 114q^{43} + 66q^{45} - 46q^{49} - 156q^{51} + 78q^{53} - 252q^{55} - 206q^{59} + 30q^{61} + 12q^{65} + 226q^{67} - 116q^{69} + 260q^{71} + 238q^{75} - 212q^{77} + 86q^{81} - 318q^{83} - 212q^{85} - 444q^{87} - 188q^{91} - 32q^{93} - 4q^{97} + 226q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(64, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
64.3.f.a $$6$$ $$1.744$$ 6.0.399424.1 None $$0$$ $$2$$ $$-2$$ $$4$$ $$q-\beta _{5}q^{3}+(-1-\beta _{1}-\beta _{3}-\beta _{5})q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(64, [\chi])$$ into lower level spaces

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