# Properties

 Label 96.4.f Level $96$ Weight $4$ Character orbit 96.f Rep. character $\chi_{96}(47,\cdot)$ Character field $\Q$ Dimension $10$ Newform subspaces $2$ Sturm bound $64$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$96 = 2^{5} \cdot 3$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 96.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$24$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$64$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(96, [\chi])$$.

Total New Old
Modular forms 56 14 42
Cusp forms 40 10 30
Eisenstein series 16 4 12

## Trace form

 $$10 q + 2 q^{3} - 2 q^{9} + O(q^{10})$$ $$10 q + 2 q^{3} - 2 q^{9} + 28 q^{19} + 46 q^{25} + 134 q^{27} - 64 q^{33} - 428 q^{43} - 266 q^{49} - 752 q^{51} + 116 q^{57} + 1636 q^{67} + 212 q^{73} + 1958 q^{75} + 154 q^{81} - 3168 q^{91} - 52 q^{97} - 4112 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(96, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
96.4.f.a $2$ $5.664$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-2})$$ $$0$$ $$-10$$ $$0$$ $$0$$ $$q+(-5+\beta )q^{3}+(23-10\beta )q^{9}-50\beta q^{11}+\cdots$$
96.4.f.b $8$ $5.664$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$12$$ $$0$$ $$0$$ $$q+(1+\beta _{2})q^{3}+\beta _{4}q^{5}-\beta _{6}q^{7}+(-9+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(96, [\chi])$$ into lower level spaces

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