# Properties

 Label 68.1.f Level $68$ Weight $1$ Character orbit 68.f Rep. character $\chi_{68}(47,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $2$ Newform subspaces $1$ Sturm bound $9$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$68 = 2^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 68.f (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$68$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$9$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(68, [\chi])$$.

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

 $$2 q - 2 q^{4} - 2 q^{5} + O(q^{10})$$ $$2 q - 2 q^{4} - 2 q^{5} + 2 q^{10} + 2 q^{16} - 2 q^{17} - 2 q^{18} + 2 q^{20} + 2 q^{29} - 2 q^{37} - 2 q^{40} + 2 q^{41} + 2 q^{45} - 2 q^{50} - 2 q^{58} - 2 q^{61} - 2 q^{64} + 2 q^{68} + 2 q^{72} + 2 q^{73} + 2 q^{74} - 2 q^{80} - 2 q^{81} + 2 q^{82} + 2 q^{85} + 2 q^{90} - 2 q^{97} + 2 q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(68, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
68.1.f.a $2$ $0.034$ $$\Q(\sqrt{-1})$$ $D_{4}$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots$$