 
Summary: COLLOQUIUM
Chris Marks
University of Alberta
The Bounded
Denominator Conjecture
for VectorValued
Modular Forms
Friday, November 26, 2010
3:30 p.m.
Mathematics and Statistics Lounge, CW 307.20
Abstract:A wellknown consequence of the theory of Hecke operators is that
modular forms for congruence subgroups of the modular group PSL2(Z) have
"bounded denominators", e.g. if f is a modular form for a congruence subgroup
whose Fourier coefficients are rational numbers, then there is some large integer
M such that the Fourier coefficients of Mf are all rational integers. Atkin and
SwinnertonDyer were the first to observe (in the early 1970s) that this prop
erty does not necessarily hold for noncongruence modular forms, and it has since
been conjectured that this property of having bounded denominators is in fact
equivalent to being a congruence modular form. Since the original paper of ASD
much work has been done in this area, but few techniques have emerged which
