Dihedral Congruence Primes and Class Fields of Real Quadratic Fields Original Research Article

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 var epsilonk−1+±1 where var epsilon+ 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.