# Properties

 Label 96.9.b Level $96$ Weight $9$ Character orbit 96.b Rep. character $\chi_{96}(79,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $1$ Sturm bound $144$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$96 = 2^{5} \cdot 3$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 96.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$144$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{9}(96, [\chi])$$.

Total New Old
Modular forms 136 16 120
Cusp forms 120 16 104
Eisenstein series 16 0 16

## Trace form

 $$16 q + 34992 q^{9} + O(q^{10})$$ $$16 q + 34992 q^{9} + 39552 q^{11} + 77280 q^{17} - 167552 q^{19} - 1604144 q^{25} + 2415744 q^{35} - 2187360 q^{41} - 3525248 q^{43} - 7109552 q^{49} - 13862016 q^{51} - 1550016 q^{57} - 44938752 q^{59} - 52558464 q^{65} - 6892544 q^{67} + 12400160 q^{73} - 12918528 q^{75} + 76527504 q^{81} + 209328000 q^{83} - 152224800 q^{89} - 395802240 q^{91} - 38799136 q^{97} + 86500224 q^{99} + O(q^{100})$$

## Decomposition of $$S_{9}^{\mathrm{new}}(96, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
96.9.b.a $16$ $39.108$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{3}q^{7}+3^{7}q^{9}+\cdots$$

## Decomposition of $$S_{9}^{\mathrm{old}}(96, [\chi])$$ into lower level spaces

$$S_{9}^{\mathrm{old}}(96, [\chi]) \cong$$ $$S_{9}^{\mathrm{new}}(8, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 2}$$