under the impression - Phrases/Idioms
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Thinking, assuming, or believing something, as in I was under the impression that they were coming today. This idiom often suggests that the idea or belief one had is mistaken. [Mid-1800s]