# Properties

 Label 44.1.d Level $44$ Weight $1$ Character orbit 44.d Rep. character $\chi_{44}(21,\cdot)$ Character field $\Q$ Dimension $1$ Newform subspaces $1$ Sturm bound $6$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$44 = 2^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 44.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$6$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(44, [\chi])$$.

Total New Old
Modular forms 4 1 3
Cusp forms 1 1 0
Eisenstein series 3 0 3

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 1 0 0 0

## Trace form

 $$q - q^{3} - q^{5} + O(q^{10})$$ $$q - q^{3} - q^{5} + q^{11} + q^{15} - q^{23} + q^{27} - q^{31} - q^{33} - q^{37} + 2 q^{47} + q^{49} + 2 q^{53} - q^{55} - q^{59} - q^{67} + q^{69} - q^{71} - q^{81} - q^{89} + q^{93} - q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(44, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
44.1.d.a $1$ $0.022$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-11})$$ None $$0$$ $$-1$$ $$-1$$ $$0$$ $$q-q^{3}-q^{5}+q^{11}+q^{15}-q^{23}+q^{27}+\cdots$$