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We construct a new family of minimal surfaces of general type withp  g   =  q  =  2    andK  2   =  6   , whose Albanese map is a quadruple cover of an abelian surface with polarization of type    (  1  ,  3  )   . We also show that this family provides an irreducible component of the moduli space of surfaces withp  g   =  q  =  2    andK  2   =  6   . Finally, we prove that such a component is generically smooth of dimension   4   and that it contains the two‐dimensional family of product–quotient examples previously constructed by the first author. The main tools we use are the Fourier–Mukai transform and the Schrödinger representation of the finite Heisenberg group    H  3   .

A new family of surfaces with p g = q =2 and K 2 =6 whose Albanese map has degree 4