Deformation of vect(1)vect(1)-modules of symbols

We consider the action of the Lie algebra of polynomial vector fields, vect(1)vect(1), by the Lie derivative on the space of symbols Sβn=⨁j=0nFβ−j. We study the deformations of this action. We exhibit explicit expressions of some 2-cocycles generating the second cohomology space Hdiff2(vect(1),Dν,μ) where Dν,μDν,μ is the space of differential operators from FνFν to FμFμ. Necessary second-order integrability conditions of any infinitesimal deformations of Sβn are given. We describe completely the formal deformations for some spaces Sβn and we give concrete examples of nontrivial deformations.