# Mathematical Sciences Research Institute

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# Seminar

Newforms and multiplicities on $\Gamma_0(9)$ March 07, 2011 (10:00 AM PST - 10:50 AM PST)
Parent Program: -- MSRI: Baker Board Room
Speaker(s) Fredrik Strömberg (University of Nottingham)
Description

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