# Properties

 Label 40.2.c Level $40$ Weight $2$ Character orbit 40.c Rep. character $\chi_{40}(9,\cdot)$ Character field $\Q$ Dimension $2$ 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.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ 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 10 2 8
Cusp forms 2 2 0
Eisenstein series 8 0 8

## Trace form

 $$2 q - 2 q^{5} - 2 q^{9} + O(q^{10})$$ $$2 q - 2 q^{5} - 2 q^{9} - 8 q^{11} + 8 q^{15} + 8 q^{19} + 8 q^{21} - 6 q^{25} - 4 q^{29} - 8 q^{35} - 16 q^{39} + 4 q^{41} + 2 q^{45} + 6 q^{49} + 8 q^{55} + 24 q^{59} - 20 q^{61} + 16 q^{65} + 8 q^{69} + 16 q^{71} - 16 q^{75} - 32 q^{79} - 22 q^{81} - 12 q^{89} + 16 q^{91} - 8 q^{95} + 8 q^{99} + O(q^{100})$$

## 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.c.a $2$ $0.319$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{3}+(-1-i)q^{5}-iq^{7}-q^{9}+\cdots$$