My oscilloscope 2432A has a noisy trace

My 2432A is working fine, except it has a slightly noisy trace. The readouts on the screen are nice and sharp but the trace lines of both channels are a bit noisy, see attached pic. Even when the inpus are grounded it does not change a thing. Any hint where to look to repair this?

The 2432A is a 300MHz scope, so it is quite normal to have some noise on the trace with nothing connected at the input.  Since this scope features a digitizer to sample the waveform, the noise appears more apparent than it would from just a live analog trace where the noise would appear muted due to the phosphor glowing brighter in the middle of the trace.