## On Maeda's conjecture I

Alex Ghitza
Mon 22 May 2017 at 11am in room 107 (Peter Hall building)

Given an even integer $k$ and a prime number $p$, we can consider the characteristic polynomial of the Hecke operator $T_p$ acting on the space of cusp forms of level one and weight $k$. Maeda conjectured that this polynomial is always irreducible and its Galois group is the symmetric group $S_d$, where $d$ is the dimension of the space of cusp forms. I will survey what is known about this conjecture, including a result of Bengoechea from March 2017.