The near-infrared integral field spectrograph SINFONI at the ESO VLT opens a new window for the study of central supermassive black holes . With a near-IR spatial resolution similar to HST optical and the ability to penetrate dust it provides the possibility to explore the low-mass end of the M _ { \bullet } - \sigma relation ( \sigma < 120 km s ^ { -1 } ) where so far very few black hole masses were measured with stellar dynamics . With SINFONI we observed the central region of the low-luminosity elliptical galaxy NGC 4486a at a spatial resolution of \approx 0.1 \arcsec in the K band . The stellar kinematics was measured with a maximum penalised likelihood method considering the region around the CO absorption band heads . We determined a black hole mass of M _ { \bullet } = ( 1.25 ^ { +0.75 } _ { -0.79 } ) \times 10 ^ { 7 } ~ { } \mathrm { M _ { \odot } } ( 90 % C.L . ) using the Schwarzschild orbit superposition method including the full 2-dimensional spatial information . This mass agrees with the predictions of the M _ { \bullet } - \sigma relation , strengthening its validity at the lower \sigma end .