# Properties

 Label 112.2.p Level $112$ Weight $2$ Character orbit 112.p Rep. character $\chi_{112}(31,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $8$ Newform subspaces $3$ Sturm bound $32$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$112 = 2^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 112.p (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$28$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ 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 44 8 36
Cusp forms 20 8 12
Eisenstein series 24 0 24

## Trace form

 $$8 q - 4 q^{9} + O(q^{10})$$ $$8 q - 4 q^{9} + 4 q^{21} - 8 q^{25} - 24 q^{29} - 36 q^{33} - 4 q^{37} + 36 q^{45} + 32 q^{49} + 12 q^{53} + 56 q^{57} + 36 q^{61} - 12 q^{65} - 12 q^{73} - 48 q^{77} + 8 q^{81} - 72 q^{85} - 36 q^{89} + 4 q^{93} + O(q^{100})$$

## 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.p.a $2$ $0.894$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$3$$ $$4$$ $$q+(-1+\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots$$
112.2.p.b $2$ $0.894$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$3$$ $$-4$$ $$q+(1-\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$$
112.2.p.c $4$ $0.894$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$0$$ $$0$$ $$-6$$ $$0$$ $$q+\beta _{1}q^{3}+(-2-\beta _{2})q^{5}-\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots$$

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

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