# Properties

 Label 44.2.c Level $44$ Weight $2$ Character orbit 44.c Rep. character $\chi_{44}(43,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $1$ Sturm bound $12$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$44 = 2^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 44.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$44$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(44, [\chi])$$.

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

## Trace form

 $$4 q - 4 q^{4} - 4 q^{5} + O(q^{10})$$ $$4 q - 4 q^{4} - 4 q^{5} + 12 q^{12} - 8 q^{14} - 8 q^{16} + 4 q^{20} + 8 q^{22} - 16 q^{25} + 24 q^{26} + 12 q^{33} - 24 q^{34} + 12 q^{37} + 8 q^{38} - 24 q^{42} - 12 q^{44} - 24 q^{48} + 4 q^{49} - 8 q^{53} + 32 q^{56} - 12 q^{60} + 32 q^{64} + 24 q^{66} + 36 q^{69} + 8 q^{70} - 32 q^{77} - 24 q^{78} + 8 q^{80} - 36 q^{81} + 24 q^{82} - 16 q^{86} - 32 q^{88} - 4 q^{89} - 36 q^{92} - 12 q^{93} + 28 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(44, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
44.2.c.a $4$ $0.351$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-1+\beta _{2})q^{4}-q^{5}+\cdots$$