Joint IAS/Princeton University Number Theory Seminar

Let K be an imaginary quadratic field. Modular forms for K are related to the cohomology of arithmetic 3-manifolds. By using the Galois representations associated to such forms we produce an explicit tower of rational homology three spheres with certain properties, answering a question of Cooper. Along the way we give the world's most complicated proof that the modular curve X_0(1) has genus zero. (Joint work with Nathan Dunfield)