# Properties

 Label 112.1.l Level $112$ Weight $1$ Character orbit 112.l Rep. character $\chi_{112}(13,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $2$ Newform subspaces $1$ Sturm bound $16$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$112 = 2^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 112.l (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$112$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$16$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(112, [\chi])$$.

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

 $$2q - 2q^{4} + O(q^{10})$$ $$2q - 2q^{4} - 2q^{11} - 2q^{14} + 2q^{16} + 2q^{18} + 2q^{22} - 2q^{29} - 2q^{37} + 2q^{43} + 2q^{44} - 2q^{49} - 2q^{50} + 2q^{53} + 2q^{56} - 2q^{58} + 2q^{63} - 2q^{64} + 2q^{67} - 2q^{72} + 2q^{74} + 2q^{77} - 2q^{81} - 2q^{86} - 2q^{88} - 2q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(112, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
112.1.l.a $$2$$ $$0.056$$ $$\Q(\sqrt{-1})$$ $$D_{4}$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}+iq^{7}-iq^{8}-iq^{9}+\cdots$$