commas?

No.

teacherJapanDoes it convey a different nuance when I put a comma there?

I would leave it out. There is not a high probability that anyone will think of a sofa which is reading a cookbook.

CJ

The comma makes what follows it seem a little less important, a little less part of the main idea.

Thank you very much for your answers!!

teacherJapan I saw my mother lying on the sofa (,) reading a cook book. Does it convey a different nuance when I put a comma there?

I think that comma is redundant here. Actually, the conjunction "and" is implied there (in the "(,)" mark position) connecting two non-finite clauses.