Magnetars have been proposed to be the origin of FRBs soon after its initial discovery. The detection of the first Galactic FRB 20200428 from SGR 1935+2154 has made this hypothesis more convincing. In October 2020, this source was supposed to be in an extremely active state again. We then carried out a 1.6-hours follow-up observation of SGR 1935+2154 using the new ultra-wideband low (UWL) receiver of the Parkes 64,m radio telescope covering a frequency range of 704$-$4032 MHz. However, no convincing signal was detected in either of our single pulse or periodicity searches. We obtained a limit on the flux density of periodic signal of $rm 3.6,mu Jy$ using the full 3.3GHz bandwidth data sets, which is the strictest limit for that of SGR 1935+2154. Our full bandwidth limit on the single pulses fluence is 35mJy ms, which is well below the brightest single pulses detected by the FAST radio telescope just two before our observation. Assuming that SGR 1935+2154 is active during our observation, our results suggest that its radio bursts are either intrinsically narrowband or show a steep spectrum.
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