Harmonic lifts of modular forms
  It is shown that each complex conjugate of a meromorphic modular form for $\mathrm{SL}_2(\mathbb{Z})$ of any complex weight $p$ occurs as the image of a harmonic modular form under the operator $2i y^p \, \partial_{\bar z}$. These harmonic lifts occur in holomorphic families with the weight as the parameter. 
Roelof W. Bruggeman
math.NT