A weighted one-level density for Dirichlet L-functions with a new type of density

In 1999 Katz and Sarnak conjectured that the distribution of low-lying zeros of L-functions in a family is similar to that of the eigenvalues of random matrices.
Recently, Sugiyama observed a new phenomenon occurring in a family of symmetric square L-functions attached to Hilbert modular forms, in which its symmetry
type changes from symplectic to a new type of density function which does not occur in the Katz-Sarnak Conjecture.
In this talk, I will introduce my recent result with Sugiyama which verifies this phenomenon in the case of Dirichlet L-functions.