# Properties

 Label 32.9.c Level $32$ Weight $9$ Character orbit 32.c Rep. character $\chi_{32}(31,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $2$ Sturm bound $36$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$32 = 2^{5}$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 32.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$36$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{9}(32, [\chi])$$.

Total New Old
Modular forms 36 8 28
Cusp forms 28 8 20
Eisenstein series 8 0 8

## Trace form

 $$8 q + 336 q^{5} - 13688 q^{9} + O(q^{10})$$ $$8 q + 336 q^{5} - 13688 q^{9} + 79952 q^{13} - 143472 q^{17} - 98048 q^{21} + 731160 q^{25} - 1196208 q^{29} + 751232 q^{33} + 1262160 q^{37} - 4010736 q^{41} + 6978128 q^{45} - 9036792 q^{49} - 6827952 q^{53} + 29794176 q^{57} - 1176496 q^{61} - 10134240 q^{65} - 69833984 q^{69} + 23856528 q^{73} + 138655488 q^{77} - 100218232 q^{81} - 35762784 q^{85} + 85400976 q^{89} + 118678528 q^{93} - 339534448 q^{97} + O(q^{100})$$

## Decomposition of $$S_{9}^{\mathrm{new}}(32, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
32.9.c.a $4$ $13.036$ $$\Q(i, \sqrt{39})$$ None $$0$$ $$0$$ $$-728$$ $$0$$ $$q+(\beta _{1}+\beta _{3})q^{3}+(-182+\beta _{2})q^{5}+(17\beta _{1}+\cdots)q^{7}+\cdots$$
32.9.c.b $4$ $13.036$ $$\Q(i, \sqrt{19})$$ None $$0$$ $$0$$ $$1064$$ $$0$$ $$q+\beta _{3}q^{3}+(266+3\beta _{2})q^{5}+(-7\beta _{1}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{9}^{\mathrm{old}}(32, [\chi])$$ into lower level spaces

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