** Eknath Ghate**

TIFR

June 27, 2013

**Modular forms and the 16-61 theorem**:
Some years ago, Duke and I independently showed that the product of two level one eigenforms is never an eigenform, except in 16 cases. Recently, Johnson showed that the same is true with no restriction on the level, with 61 exceptions. This talk will introduce some of the basic definitions and results in the theory of modular forms, against the backdrop of the 16-61 theorm.