# Properties

 Label 40.2.k Level $40$ Weight $2$ Character orbit 40.k Rep. character $\chi_{40}(3,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $8$ Newform subspaces $1$ Sturm bound $12$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$40 = 2^{3} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 40.k (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$40$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(40, [\chi])$$.

Total New Old
Modular forms 16 16 0
Cusp forms 8 8 0
Eisenstein series 8 8 0

## Trace form

 $$8 q - 2 q^{2} - 4 q^{3} - 8 q^{6} + 4 q^{8} + O(q^{10})$$ $$8 q - 2 q^{2} - 4 q^{3} - 8 q^{6} + 4 q^{8} - 10 q^{10} - 8 q^{11} + 12 q^{12} + 8 q^{16} - 8 q^{17} + 10 q^{18} + 12 q^{22} + 20 q^{26} + 8 q^{27} - 20 q^{28} + 20 q^{30} - 32 q^{32} - 16 q^{33} + 20 q^{35} - 20 q^{36} - 4 q^{38} - 20 q^{40} - 8 q^{41} - 20 q^{42} + 28 q^{43} - 40 q^{46} + 16 q^{48} - 10 q^{50} + 8 q^{51} + 20 q^{52} + 40 q^{56} + 8 q^{57} + 20 q^{58} + 20 q^{60} + 40 q^{62} + 8 q^{66} - 28 q^{67} - 4 q^{68} + 20 q^{70} - 20 q^{72} + 16 q^{73} - 60 q^{75} - 8 q^{76} - 40 q^{78} + 32 q^{81} - 28 q^{82} - 44 q^{83} - 24 q^{86} + 16 q^{88} - 10 q^{90} - 40 q^{91} + 20 q^{92} + 32 q^{96} + 16 q^{97} - 6 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(40, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
40.2.k.a $8$ $0.319$ $$\Q(\zeta_{20})$$ None $$-2$$ $$-4$$ $$0$$ $$0$$ $$q-\zeta_{20}^{7}q^{2}+(-1+\zeta_{20}^{3}+\zeta_{20}^{5}+\cdots)q^{3}+\cdots$$