On uniform large Galois images for modular abelian varieties
  We formulate a question regarding uniform versions of "large Galois image properties" for modular abelian varieties of higher dimension, generalizing the well-known case of elliptic curves. We then answer our question affirmatively in the exceptional image case, and provide lower estimates for uniform bounds in the remaining cases. 
Eknath Ghate, Pierre Parent
math.NT