BASES FOR S-k(Gamma(1)(4)) AND FORMULAS FOR EVEN POWERS OF THE JACOBI THETA FUNCTION

Abstract

We find a basis for the space S-k(Gamma(1)(4)) of cusp forms of weight k for the congruence subgroup G1(4) in terms of Eisenstein series. As an application, we obtain formulas for r(2k)(n), the number of ways to represent a non-negative integer n as sums of 2k integer squares.