Milner 317

Wednesdays, 12:30-1:30 PM

Texas A&M University

**Wednesday, October 12
Milner 317, 12:30 PM**

**Title:** *An exposition of "Hecke Operators on Gamma_0(m)" by Atkin
and Lehner*

**Abstract:** In this talk, we'll be discussing the very important
and beautiful paper of Atkin and Lehner in which they describe the
action of the Hecke operators on Gamma_0(m) (including the ones
dividing the level, which coincide with the "U-operators"). The main
results of the paper describe certain subspaces of cusp forms that
have basis of simultaneous eigenforms of every operator in sight
(including T_p, U_q and the "Atkin-Lehner" operators). Certain
striking properties of the coefficients of such eigenforms are
described. The background assumed for the talk will be little beyond
the definition of modular and cusp forms.