# Properties

 Label 96.2.d Level $96$ Weight $2$ Character orbit 96.d Rep. character $\chi_{96}(49,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $32$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$96 = 2^{5} \cdot 3$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 96.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$32$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(96, [\chi])$$.

Total New Old
Modular forms 24 2 22
Cusp forms 8 2 6
Eisenstein series 16 0 16

## Trace form

 $$2q + 4q^{7} - 2q^{9} + O(q^{10})$$ $$2q + 4q^{7} - 2q^{9} - 4q^{15} - 4q^{17} - 8q^{23} + 2q^{25} - 4q^{31} + 8q^{39} + 4q^{41} + 24q^{47} - 6q^{49} + 8q^{57} - 4q^{63} + 16q^{65} - 24q^{71} - 12q^{73} - 20q^{79} + 2q^{81} + 12q^{87} - 20q^{89} + 16q^{95} - 4q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(96, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
96.2.d.a $$2$$ $$0.767$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+iq^{3}+2iq^{5}+2q^{7}-q^{9}-4iq^{13}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(96, [\chi])$$ into lower level spaces

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