  We use the theory of topological modular forms to constrain bosonic
holomorphic CFTs, which can be viewed as $(0,1)$ SCFTs with trivial
right-moving supersymmetric sector. A conjecture by Segal, Stolz and Teichner
requires the constant term of the partition function to be divisible by
specific integers determined by the central charge. We verify this constraint
in large classes of physical examples, and rule out the existence of an
infinite set of extremal CFTs, including those with central charges $c=48, 72,
96$ and $120$.
