Revisiting the modularity of the abelian surfaces of conductor 277

There is an isogeny class of semistable abelian surfaces A with good reduction outside 277 and End_Q(A) = Z. The modularity (or paramodularity) of this class was proved by a team of six people: Armand Brumer, Ariel Pacetti, Cris Poor, Gonzalo Tornaria, John Voight and David Yuen. They did so by using the so-called Faltings-Serre method. This was the first known case of the paramodularity conjecture. In this work in progress, I will discuss how to (re-)prove the modularity of these surfaces by directly applying deformation theory. This could be seen as an explicit approach to deformation theory.