Mathematics

Dr. Manami Roy
University of Oklahoma

There is a lifting from a non-CM elliptic curve over $\\Q$ to a paramodular form (a Siegel modular form with respect to the paramodular group) of degree 2 and weight 3 such that the spin L-function of the paramodular form is equal to the symmetric cube L-function of the given elliptic curve. We find the level of the paramodular form in an explicit and elementary way in terms of the coefficients of the Weierstrass equation of the given elliptic curve. In order to understand this lifting and to find an explicit formula for the level, we will discuss the underlying representation theoretic mechanism.