Generalised Kummer constructions and Weil restrictions

Understand

We use a generalised Kummer construction to realise all but one known weight four newforms with complex multiplication and rational Fourier coefficients in smooth Calabi-Yau threefolds defined over the rational numbers.

• The Calabi-Yau manifolds are smooth models of quotients of the Weil restrictions of elliptic curves with CM of class number three.