Modular forms on and

The characters are generated by the character , where . Let . Then K has class number 1, discriminant -3, and the ring of integers is , where . There are 6 units. If we put then N(x+yr)=Q(x,y). For each n>0 we can define an algebraic Hecke character modulo the ideal m=(1+r) by for . We denote the Hecke L-function with Grössencharakter by

where the sum is over the ideals of . Since if and only if 3|x-y we can rewrite this as

We have , the space being spanned by oldforms.