Ling Long (Iowa)
Noncongruence modular forms and modularity
Among all finite index subgroups of the modular group, majority of
them are noncongruence. Despite their lack of effective Hecke operators,
noncongruence modular forms have many algebraic and arithmetic structures.
In particular, Scholl constructed Galois representations attached to
noncongruence cuspforms under some general assumptions. In this talk, we
will discuss several modularity results which relate Galois representations
attached to noncongruence cuspforms to classical automorphic forms as well
as applications and open questions.