# Properties

 Label 24.2.d Level $24$ Weight $2$ Character orbit 24.d Rep. character $\chi_{24}(13,\cdot)$ 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.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ 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 2 4
Cusp forms 2 2 0
Eisenstein series 4 0 4

## Trace form

 $$2 q - 2 q^{2} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 2 q^{9} + O(q^{10})$$ $$2 q - 2 q^{2} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 2 q^{9} + 4 q^{10} + 4 q^{12} + 4 q^{14} + 4 q^{15} - 8 q^{16} - 4 q^{17} + 2 q^{18} - 8 q^{20} + 8 q^{23} - 4 q^{24} + 2 q^{25} - 8 q^{26} - 4 q^{30} + 4 q^{31} + 8 q^{32} + 4 q^{34} + 8 q^{38} - 8 q^{39} + 8 q^{40} + 4 q^{41} + 4 q^{42} - 8 q^{46} - 24 q^{47} - 6 q^{49} - 2 q^{50} + 16 q^{52} + 2 q^{54} - 8 q^{56} + 8 q^{57} - 12 q^{58} - 4 q^{62} + 4 q^{63} + 16 q^{65} - 8 q^{70} + 24 q^{71} - 4 q^{72} - 12 q^{73} + 16 q^{74} - 16 q^{76} + 8 q^{78} + 20 q^{79} + 2 q^{81} - 4 q^{82} - 8 q^{84} - 8 q^{86} - 12 q^{87} - 20 q^{89} - 4 q^{90} + 24 q^{94} - 16 q^{95} + 8 q^{96} - 4 q^{97} + 6 q^{98} + O(q^{100})$$

## 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.d.a $2$ $0.192$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$0$$ $$0$$ $$-4$$ $$q+(-1+i)q^{2}+iq^{3}-2iq^{4}-2iq^{5}+\cdots$$