Dihedral congruence primes and class fields of real quadratic fields

Abstract

We show that for a real quadratic field F the dihedral congruence primes with respect to F for cusp forms of weight k and quadratic nebentypus are essentially the primes dividing expressions of the form ε^k−1₊±1 where ε₊ is a totally positive fundamental unit of F. This extends work of Hida. Our results allows us to identify a family of (ray) class fields of F which are generated by torsion points on modular abelian varieties.