A basis for \(S_k(\Gamma_0(4))\) and representations of integers as sums of squares
In an earlier paper [Math. Proc. Camb. Philos. Soc. 146, No. 2, 321--350 (2009; Zbl 1205.11052)] the authors gave a basis for the space \(S_{k}(\Gamma_{0}(2))\) of cusp forms of even weight \(k\) for the congruence subgroup \(\Gamma_{0}(2)\) in terms of normalized Eisenstein series. This paper does the same for \(S_{k}(\Gamma_{0}(4))\) and applies the results to obtain formulas for the generating function of \(r_{4s}(n)\), the number of representations of \(n\) as a sum of \(4s\) integral squares.
scientific article; zbMATH DE number 6084534
scientific article