On the motive of Kummer varieties associated to $\Gamma_1(7)$ -   Supplement to the paper: The modularity of certain non-rigid Calabi-Yau   threefolds (by R. Livn\'e and N. Yui)
  In their paper Livn\'e and Yui (math.AG/0304497) discuss several examples of non-rigid Calabi-Yau varieties which admit semi-stable K3-fibrations with 6 singular fibres over a base which is a rational modular curve. They also establish the modularity of the L-function of these examples. The purpose of this note is to point out that the examples which were listed in their paper, but which do not lead to semi-stable fibrations, are still modular in the sense that their L-function is associated to modular forms. We treat the case associated to the group Gamma_1(7) in detail, but our technique also applies to many other cases. We further make some comments concerning the Kummer construction for fibre products of elliptic surfaces in general. 
Klaus Hulek and Helena Verrill