# Properties

 Label 96.9.g Level $96$ Weight $9$ Character orbit 96.g Rep. character $\chi_{96}(31,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $2$ Sturm bound $144$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$96 = 2^{5} \cdot 3$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 96.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$144$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$

## 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

 $$16 q - 672 q^{5} - 34992 q^{9} + O(q^{10})$$ $$16 q - 672 q^{5} - 34992 q^{9} - 108512 q^{13} + 231840 q^{17} - 243648 q^{21} + 1675056 q^{25} - 137760 q^{29} - 1840320 q^{33} - 3078240 q^{37} - 232032 q^{41} + 1469664 q^{45} - 13579248 q^{49} + 28130784 q^{53} + 1550016 q^{57} + 10550944 q^{61} + 13301952 q^{65} + 2829600 q^{73} - 230503680 q^{77} + 76527504 q^{81} + 82126272 q^{85} - 109134816 q^{89} - 40212288 q^{93} + 300477472 q^{97} + O(q^{100})$$

## 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.g.a $8$ $39.108$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$0$$ $$-1232$$ $$0$$ $$q+\beta _{1}q^{3}+(-154+\beta _{6})q^{5}+(17\beta _{1}+\cdots)q^{7}+\cdots$$
96.9.g.b $8$ $39.108$ 8.0.3468738816.6 None $$0$$ $$0$$ $$560$$ $$0$$ $$q+\beta _{2}q^{3}+(70+\beta _{4})q^{5}+(-7\beta _{1}-7\beta _{3}+\cdots)q^{7}+\cdots$$

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

$$S_{9}^{\mathrm{old}}(96, [\chi]) \cong$$ $$S_{9}^{\mathrm{new}}(4, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 2}$$