Let $k\geq 2$ be an even integer and let $\Gamma=\Gamma_0(N)$. Let $f\in S_k(\Gamma)$. To $f$, one may associate an antiholomorphic cusp form of weight $k$ and level $\Gamma$ by defining $g(z):=f(-\bar{z})$. These satisfy the transformation property

$$g(\gamma z)=(c\bar{z}+d)^kg(z)\qquad \gamma\in\Gamma.$$

There is a related discussion here.

Denoting the space of such objects by $\overline{S_k(\Gamma)}$, it is clear that $S_k(\Gamma)\neq0$ iff $\overline{S_k(\Gamma)}\neq 0$.

I would like to know what happens in the situation $k\leq -2$. Clozel mentions this case in his article "Motifs et formes automorphes", on page 91, where he talks of the antiholomorphic case. Given an element of $\overline{S_k(\Gamma)}$, we can, by the above procedure, get a holomorphic cusp form. If $k<0$ then $S_k(\Gamma)=0$, so will this case ($k\leq -2$) ever occur?

**EDIT**: The definition $g(z):=\overline{f(z)}$ has the advantage of avoiding the restriction put above that the integer $k$ is even.