Momentum-resolved magnetotunneling spectroscopy is performed at a single sharp quantum Hall (QH) edge to probe the structure of integer QH edge modes. An epitaxially overgrown cleaved edge is shown to realize the sharp-edge limit with interchannel distances smaller than both the magnetic length and the Bohr radius where the Chklovskii soft-edge picture is no longer valid. The line shape of principal conductance peaks is explained, and an edge filling factor is determined from the peak position. A step in the dispersion is attributed to fluctuations in the QH ground energy.