# Properties

 Label 64.9.c Level $64$ Weight $9$ Character orbit 64.c Rep. character $\chi_{64}(63,\cdot)$ Character field $\Q$ Dimension $15$ Newform subspaces $6$ Sturm bound $72$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$64 = 2^{6}$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 64.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$72$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{9}(64, [\chi])$$.

Total New Old
Modular forms 70 17 53
Cusp forms 58 15 43
Eisenstein series 12 2 10

## Trace form

 $$15 q + 2 q^{5} - 28433 q^{9} + O(q^{10})$$ $$15 q + 2 q^{5} - 28433 q^{9} - 51390 q^{13} - 77282 q^{17} - 256768 q^{21} + 505229 q^{25} + 1066178 q^{29} - 1639552 q^{33} - 1928702 q^{37} - 4938530 q^{41} - 13044158 q^{45} - 7411889 q^{49} - 9916798 q^{53} + 7071360 q^{57} + 40770242 q^{61} + 21835580 q^{65} + 65021696 q^{69} - 3806882 q^{73} - 135634176 q^{77} + 19187279 q^{81} - 38526972 q^{85} + 28472542 q^{89} + 230724608 q^{93} - 123027042 q^{97} + O(q^{100})$$

## Decomposition of $$S_{9}^{\mathrm{new}}(64, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
64.9.c.a $1$ $26.072$ $$\Q$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$1054$$ $$0$$ $$q+1054q^{5}+3^{8}q^{9}+478q^{13}-63358q^{17}+\cdots$$
64.9.c.b $2$ $26.072$ $$\Q(\sqrt{-39})$$ None $$0$$ $$0$$ $$-1220$$ $$0$$ $$q-\beta q^{3}-610q^{5}+14\beta q^{7}-3423q^{9}+\cdots$$
64.9.c.c $2$ $26.072$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-516$$ $$0$$ $$q-\zeta_{6}q^{3}-258q^{5}+238\zeta_{6}q^{7}+6369q^{9}+\cdots$$
64.9.c.d $2$ $26.072$ $$\Q(\sqrt{-35})$$ None $$0$$ $$0$$ $$1020$$ $$0$$ $$q-\beta q^{3}+510q^{5}-18\beta q^{7}-13599q^{9}+\cdots$$
64.9.c.e $4$ $26.072$ $$\Q(i, \sqrt{19})$$ None $$0$$ $$0$$ $$-1064$$ $$0$$ $$q+\beta _{3}q^{3}+(-266-3\beta _{2})q^{5}+(7\beta _{1}+\cdots)q^{7}+\cdots$$
64.9.c.f $4$ $26.072$ $$\Q(i, \sqrt{39})$$ None $$0$$ $$0$$ $$728$$ $$0$$ $$q+(\beta _{1}+\beta _{3})q^{3}+(182-\beta _{2})q^{5}+(-17\beta _{1}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{9}^{\mathrm{old}}(64, [\chi])$$ into lower level spaces

$$S_{9}^{\mathrm{old}}(64, [\chi]) \cong$$ $$S_{9}^{\mathrm{new}}(4, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 2}$$