# Properties

 Label 112.2.f Level $112$ Weight $2$ Character orbit 112.f Rep. character $\chi_{112}(111,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $2$ Sturm bound $32$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$112 = 2^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 112.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$28$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$32$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(112, [\chi])$$.

Total New Old
Modular forms 22 4 18
Cusp forms 10 4 6
Eisenstein series 12 0 12

## Trace form

 $$4q + 4q^{9} + O(q^{10})$$ $$4q + 4q^{9} - 16q^{21} - 28q^{25} + 24q^{29} - 8q^{37} + 4q^{49} + 24q^{53} + 16q^{57} + 48q^{65} - 24q^{77} - 44q^{81} - 64q^{93} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(112, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
112.2.f.a $$2$$ $$0.894$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-4$$ $$0$$ $$4$$ $$q-2q^{3}-2\zeta_{6}q^{5}+(2-\zeta_{6})q^{7}+q^{9}+\cdots$$
112.2.f.b $$2$$ $$0.894$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$4$$ $$0$$ $$-4$$ $$q+2q^{3}+2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(112, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(112, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 3}$$