Let f be a cuspidal eigenform of level N and weight k. For an odd prime p not dividing N, the local Galois representation r:GQp-->GL2(Qpbar) attached to f determines a point on the crystalline deformation ring R_rbar(k) associated with its reduction rbar:GQp-->GL2(Fpbar). The Qpbar points of this ring parametrize crystalline lifts of rbar with Hodge--Tate weights (0,k-1).
In his proof of the Fontaine--Mazur conjecture for GL2, Kisin shows that every irreducible component of R_rbar(k) contains a point arising from an eigenform of level N. We ask how these modular points are distributed among the irreducible components. In this talk, we give a formula for the number of such points on each component in terms of the geometry of its mod-p reduction and some global seed data. As an application, we prove that the number of formally smooth components of R_rbar(k) grows linearly in k when rbar is a very generic point on the underlying reduced Emerton--Gee stack and p >= 11. This is joint work with John Bergdall and Brandon Levin.