Working for a US company remotely from India during the summer, on F1 Visa

[Mohith77]

I have completed one semester (spring) of study in the US (on an F1 visa) and have returned to India for the summer break. I'm not eligible for CPT until I complete two semesters in the US.
While on Indian soil during summer break, am I allowed to do unpaid remote work for a U.S. company?