[xanmas]

Don't worry, I felt the same when I was starting to read papers as a graduate student but I came to realize that in cases like the one where you mentioned elliptic modular forms being introduced to vastly overcomplicate something, it was usually done to make something true in a far more general set of space.

For me in physics? That came about when I started reading papers where people were doing stuff with differential geometry on manifolds. I couldn't, for the life of me, figure out why people would talk about a wedge product when a cross product would have sufficed until about 6 months later when it clicked that doing something in a coordinate agnostic framework allows you to prove things for any coordinate system and create general formulas that just need a few things "plugged in."

I'm not going to pretend to know that that's why elliptical modular forms are being used in your context but everytime something has seemed needlessly overcomplicated, I've come to realize after some thinking that it's done with a view towards generality.