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 $X(N)$.