Level 7

Weights: 1 2 3 4 5 6 7 8

Modular forms on and

Let denote the real nontrivial character . In terms of the Legendre symbol, . The characters are generated by the character , where . Let . Then K has class number 1, discriminant -7, and the ring of integers is , where . For each even n>0 we can define an algebraic Hecke character of weight n by for . We denote the Hecke L-function with Grössencharakter by

where the first sum is over all ideals of .