Eisenstein series of weight 1

Special Number Theory Seminar
Topic:Eisenstein series of weight 1
Speaker:Kamal Khuri-Makdisi
Affiliation:American University of Beirut
Date:Tuesday, March 25
Time/Room:3:30pm - 4:30pm/Fine 1201, Princeton University

Let \(N \geq 3\). 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 \(X(N)\).