Losing internet connection when printing

Earlier this year, I upgraded my Cox service to include telephone and was issued an Arris TM3402A modem. Every time I use my printer, whether to print, scan, or copy, the modem loses its internet connection. The printer was originally connected wirelessly, so I disabled the wifi connection and connected it directly to a computer, but that didn't solve the issue. I recently got a new printer, but the problem continues. I reboot the modem and everything is fine until the printer powers up. Does anyone have a similar issue? Are there any suggestions/solutions out there? Thanks!