# Properties

 Label 24.2.f Level $24$ Weight $2$ Character orbit 24.f Rep. character $\chi_{24}(11,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $8$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$24 = 2^{3} \cdot 3$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 24.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$24$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$8$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(24, [\chi])$$.

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

## Trace form

 $$2 q - 2 q^{3} - 4 q^{4} + 4 q^{6} - 2 q^{9} + O(q^{10})$$ $$2 q - 2 q^{3} - 4 q^{4} + 4 q^{6} - 2 q^{9} + 4 q^{12} + 8 q^{16} - 8 q^{18} + 4 q^{19} - 8 q^{22} - 8 q^{24} - 10 q^{25} + 10 q^{27} + 8 q^{33} + 16 q^{34} + 4 q^{36} - 20 q^{43} - 8 q^{48} + 14 q^{49} - 16 q^{51} + 4 q^{54} - 4 q^{57} - 16 q^{64} + 8 q^{66} + 28 q^{67} + 16 q^{72} + 4 q^{73} + 10 q^{75} - 8 q^{76} - 14 q^{81} - 32 q^{82} + 16 q^{88} + 16 q^{96} - 20 q^{97} - 16 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(24, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
24.2.f.a $2$ $0.192$ $$\Q(\sqrt{-2})$$ $$\Q(\sqrt{-2})$$ $$0$$ $$-2$$ $$0$$ $$0$$ $$q+\beta q^{2}+(-1-\beta )q^{3}-2q^{4}+(2-\beta )q^{6}+\cdots$$