A simple method to extract zeros of certain Eisenstein series of small level

Abstract

This paper provides a simple method to extract the zeros of some weight two Eisenstein series of level N where $$N=2,3,5$$ and 7. The method is based on the observation that these Eisenstein series are integral over the graded algebra of modular forms on SL(2, Z) and their zeros are ‘controlled’ by those of $$E_4$$ and $$E_6$$ in the fundamental domain of $$\Gamma _0(N)$$ .