Oh yeah that's a nice observation! Protective space in 2D is the same as the Riemann sphere, which is the complex plane with one point added at infinity. I for

Oh yeah that's a nice observation! Protective space in 2D is the same as the Riemann sphere, which is the complex plane with one point added at infinity. I forgot to add to my post that, SL(2) is the symmetry group of the Riemann sphere. So since you often use this as your space in complex analysis, this symmetry transformation is everywhere. So that's one reason why you might expect to see modular forms in lots of places. (At least, that's what I understood, maybe a mathematician would tell you differently.)