# Eisenstein series of weight 1

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Kamal Khuri-Makdisi , American University of Beirut
Fine Hall 1201

Let N >= 3. In this talk, I will sketch a proof that the ring generated by Eisenstein series of weight 1 on the principal congruence subgroup Gamma(N) contains all modular forms in weights 2 and above. This means that the only forms that are not seen by polynomials in these Eisenstein series are cusp forms of weight 1. This result gives rise to a systematic way to produce equations for the modular curve X(N).