TITLE: Langlands in dimension 2: the Yoshida conjecture
QUESTION [44 upvotes]: Background:
One prominent part of the Langlands program is the conjecture that
  all motives are automorphic.
  It is of interest to consider special cases that are more precise, if less
  sweeping. The idea is to formulate generalized modularity conjectures
  that are as concrete as the Shimura-Taniyama-Weil conjecture
  (now the elliptic modularity theorem). The latter gained much in
  precision, for example, by Weil's experimental observation of the link between
  the conductor of the elliptic curve and the level of the weight two
  modular form. As a next step up the dimension ladder it is natural to consider
  abelian surfaces over ${\mathbb Q}$, in which case one encounters
Yoshida's conjecture:
 Any irreducible abelian surface $A$ defined over ${\mathbb Q}$ and with End$(A)={\mathbb Z}$ is modular in the sense that associated to each is a holomorphic Siegel modular
    cusp eigenform $F$ of genus 2, weight 2, and some level $N$, such
    that its spinor L-function $L_{\rm spin}(F,s)$ agrees with that of the 
    abelian surface
     $$
     L(H^1(A),s) ~=~ L_{\rm spin}(F,s).
     $$
Questions:

Has Yoshida's conjecture been proven for some classes of
 abelian surfaces over ${\mathbb Q}$?
Are there lists of abelian surfaces and associated Siegel modular forms that extend the very useful lists constructed by Cremona and Stein for elliptic curves and their associated modular forms?

REPLY [5 votes]: And so it turns out that I was in the audience of a seminar talk just today on this very subject. The opinion I expressed in comments is apparently not too far from the truth: V.Pilloni and B.Stroh now have some variants of Coleman's criterion for classicality for $\textrm{GSp}_{4}$, and so full modularity for some abelian surfaces is now accessible. So the answer to your question 1 seems to be yes, but you need to rely on cutting edge results to really get these kind of results.
Check out the joint works of V.Pilloni and B.Stroh.