# Properties

 Label 68.1.d Level $68$ Weight $1$ Character orbit 68.d Rep. character $\chi_{68}(67,\cdot)$ Character field $\Q$ Dimension $1$ 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.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$68$$ Character field: $$\Q$$ 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 3 3 0
Cusp forms 1 1 0
Eisenstein series 2 2 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 1 0 0 0

## Trace form

 $$q - q^{2} + q^{4} - q^{8} - q^{9} + O(q^{10})$$ $$q - q^{2} + q^{4} - q^{8} - q^{9} - 2 q^{13} + q^{16} + q^{17} + q^{18} + q^{25} + 2 q^{26} - q^{32} - q^{34} - q^{36} - q^{49} - q^{50} - 2 q^{52} + 2 q^{53} + q^{64} + q^{68} + q^{72} + q^{81} - 2 q^{89} + q^{98} + O(q^{100})$$

## 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.d.a $1$ $0.034$ $$\Q$$ $D_{2}$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-17})$$ $$\Q(\sqrt{17})$$ $$-1$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+q^{4}-q^{8}-q^{9}-2q^{13}+q^{16}+\cdots$$