# Properties

 Label 64.8.e Level $64$ Weight $8$ Character orbit 64.e Rep. character $\chi_{64}(17,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $26$ Newform subspaces $1$ Sturm bound $64$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$64 = 2^{6}$$ Weight: $$k$$ $$=$$ $$8$$ 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: $$64$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 120 30 90
Cusp forms 104 26 78
Eisenstein series 16 4 12

## Trace form

 $$26 q + 2 q^{3} - 2 q^{5} + O(q^{10})$$ $$26 q + 2 q^{3} - 2 q^{5} - 1202 q^{11} - 2 q^{13} + 27004 q^{15} - 4 q^{17} - 60582 q^{19} + 4372 q^{21} + 233672 q^{27} - 51690 q^{29} - 357488 q^{31} - 4 q^{33} + 252004 q^{35} + 415574 q^{37} - 569754 q^{43} + 151874 q^{45} + 2076464 q^{47} - 1647090 q^{49} - 2609508 q^{51} + 907814 q^{53} + 4865142 q^{59} + 2279886 q^{61} - 8295108 q^{63} - 1426892 q^{65} + 5564458 q^{67} - 4786076 q^{69} - 6212566 q^{75} + 7604308 q^{77} + 9598912 q^{79} - 5314414 q^{81} - 4531198 q^{83} + 7377748 q^{85} - 2587652 q^{91} - 14504144 q^{93} + 4900620 q^{95} - 4 q^{97} - 18815006 q^{99} + O(q^{100})$$

## 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.e.a $26$ $19.993$ None $$0$$ $$2$$ $$-2$$ $$0$$

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

$$S_{8}^{\mathrm{old}}(64, [\chi]) \cong$$ $$S_{8}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 3}$$