  We study multifractal spectra of critical wave functions at the integer
quantum Hall plateau transition using the Chalker-Coddington network model. Our
numerical results provide important new constraints which any critical theory
for the transition will have to satisfy. We find a non-parabolic multifractal
spectrum and we further determine the ratio of boundary to bulk multifractal
exponents. Our results rule out an exactly parabolic spectrum that has been the
centerpiece in a number of proposals for critical field theories of the
transition. In addition, we demonstrate analytically exact parabolicity of
related boundary spectra in the 2D chiral orthogonal `Gade-Wegner' symmetry
class.
