# Properties

 Label 96.3.e Level $96$ Weight $3$ Character orbit 96.e Rep. character $\chi_{96}(65,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $2$ Sturm bound $48$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$96 = 2^{5} \cdot 3$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 96.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$48$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(96, [\chi])$$.

Total New Old
Modular forms 40 8 32
Cusp forms 24 8 16
Eisenstein series 16 0 16

## Trace form

 $$8 q + 8 q^{9} + O(q^{10})$$ $$8 q + 8 q^{9} + 16 q^{13} + 16 q^{21} - 56 q^{25} - 64 q^{33} - 112 q^{37} - 128 q^{45} + 152 q^{49} + 208 q^{57} + 272 q^{61} + 384 q^{69} - 240 q^{73} - 376 q^{81} - 256 q^{85} - 496 q^{93} + 400 q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(96, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
96.3.e.a $4$ $2.616$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(2\beta _{1}-\beta _{3})q^{7}+(-3+\cdots)q^{9}+\cdots$$
96.3.e.b $4$ $2.616$ $$\Q(\sqrt{-2}, \sqrt{7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{3})q^{3}-\beta _{2}q^{5}+(-\beta _{1}-2\beta _{3})q^{7}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(96, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(96, [\chi]) \simeq$$ $$S_{3}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 2}$$