Eisenstein series identities based on partial fraction decomposition

摘要

From the theory of modular forms, we know that there are exactly [(k-2)/6] linear relations among the Eisenstein series E-k and its products E-2i E-k-(2i) (2 <= i <= [k/4]). We present explicit formulas among these modular forms based on the partial fraction decomposition, and use them to determine a basis for the space of modular forms of weight on k on SL2(Z).