# Properties

 Label 1444.1.h Level $1444$ Weight $1$ Character orbit 1444.h Rep. character $\chi_{1444}(69,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $6$ Newform subspaces $2$ Sturm bound $190$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1444 = 2^{2} \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1444.h (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$190$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1444, [\chi])$$.

Total New Old
Modular forms 66 6 60
Cusp forms 6 6 0
Eisenstein series 60 0 60

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 4 0

## Trace form

 $$6 q - q^{5} + 2 q^{7} + q^{9} + O(q^{10})$$ $$6 q - q^{5} + 2 q^{7} + q^{9} - 6 q^{11} - q^{17} - 2 q^{23} - 3 q^{35} + 3 q^{43} - 6 q^{45} + 3 q^{47} + q^{55} + 3 q^{61} + 3 q^{63} - q^{73} - 2 q^{77} + q^{81} + 4 q^{83} - 3 q^{85} + 8 q^{87} - q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1444, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1444.1.h.a $2$ $0.721$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$1$$ $$-2$$ $$q-\zeta_{6}^{2}q^{5}-q^{7}-\zeta_{6}q^{9}-q^{11}-\zeta_{6}^{2}q^{17}+\cdots$$
1444.1.h.b $4$ $0.721$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ $S_{4}$ None None $$0$$ $$0$$ $$-2$$ $$4$$ $$q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+q^{7}+\beta _{2}q^{9}+\cdots$$