# Properties

 Label 96.3.b Level $96$ Weight $3$ Character orbit 96.b Rep. character $\chi_{96}(79,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $1$ Sturm bound $48$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$96 = 2^{5} \cdot 3$$ Weight: $$k$$ $$=$$ $$3$$ 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: $$48$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 40 4 36
Cusp forms 24 4 20
Eisenstein series 16 0 16

## Trace form

 $$4q + 12q^{9} + O(q^{10})$$ $$4q + 12q^{9} + 32q^{11} - 8q^{17} - 32q^{19} - 44q^{25} - 96q^{35} + 40q^{41} - 32q^{43} - 44q^{49} + 96q^{51} - 48q^{57} + 128q^{59} + 96q^{65} + 256q^{67} + 200q^{73} - 192q^{75} + 36q^{81} - 160q^{83} - 200q^{89} - 288q^{91} + 56q^{97} + 96q^{99} + O(q^{100})$$

## 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.b.a $$4$$ $$2.616$$ 4.0.4752.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+\cdots$$

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

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