# Properties

 Label 111.1.h Level $111$ Weight $1$ Character orbit 111.h Rep. character $\chi_{111}(11,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $2$ Newform subspaces $1$ Sturm bound $12$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$111 = 3 \cdot 37$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 111.h (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$111$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(111, [\chi])$$.

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

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

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

## Trace form

 $$2 q - q^{3} + q^{4} - q^{7} - q^{9} + O(q^{10})$$ $$2 q - q^{3} + q^{4} - q^{7} - q^{9} + q^{12} - 3 q^{13} - q^{16} - q^{21} + q^{25} + 2 q^{27} + q^{28} - 2 q^{36} + 2 q^{37} + 3 q^{39} + 2 q^{48} - 3 q^{52} + 2 q^{63} - 2 q^{64} - q^{67} + 2 q^{73} - 2 q^{75} - 3 q^{79} - q^{81} - 2 q^{84} + 3 q^{91} - 3 q^{93} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(111, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
111.1.h.a $2$ $0.055$ $$\Q(\sqrt{-3})$$ $D_{6}$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$-1$$ $$q-\zeta_{6}q^{3}+\zeta_{6}q^{4}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$$