Identities Arising From Hecke Transformations of Modular Forms Over Q( ) and Q( )

The Hecke transform is used on Hilbert modular forms over Q( ) and Q ( ) to produce unusual numerical identities. The case for Q( ) is complicated by the fact that there are two spaces of modular forms. The computer algebra system MACSYMA was used to find eigenfunctions of the Hecke transform, and to calculate identities involving the analogue of the sum of divisors functions.