Location: Baker Boardroom
Speaker: Fredrik Stroemberg
Title: Newforms and multiplicities on $Gamma_0(9)$
A curious fact about the group $Gamma_0(9)$ is that it does not possess
any "truly new" modular forms, by this we mean that all modular forms
are lifts or twists coming from lower levels. For holomorphic modular
forms this can be proved using standard dimension formulas together with
an an auxiliary group of level 3 and some lemmas about twists.
For Maass waveforms, which we will treat in this talk, one has instead
to use the Selberg trace formula.
The motivation for the investigations during which I stumbled over this
fact was to explain the experimentally found multiplicities in the new
part (in the sense of Atkin-Lehner) of the Laplace spectrum on
$Gamma_0(9)$. It turns out that these multiplicities arise from pairs
of forms which are twists of each other and I will also show how to
prove the existence of such pairs.