A surprising property of the cohomology of locally symmetric spaces is that Hecke operators can act on multiple cohomological degrees with the same eigenvalues. A recent series of conjectures proposes an arithmetic explanation: a hidden degree-shifting action of a certain motivic cohomology group. We will give an overview of the conjectures of Venkatesh, Prasanna, and Harris, and discuss our own conjecture for Hilbert modular forms of parallel weight one. Speaker(s): Aleksander Horawa (University of Michigan)