A modem does not store data, it has no memory to fill. It simply converts the signal from one form to another. Modem is short for modulator - demodulator.
I suggest calling your ISP support line for assistance as that message is non-seniscal - please note: I have provided tech support for several years dealing with digital communication for several different technologies in-cluding Dial-Up, DSL, and Broadband Over Powerline in addition to local Ethernet and Token-Ring technologies. I have never heard of or encountered the error you describe or a modem's memory being full - since it has no memory ...