under the impression

Prepositional phrase

followed by a clause idiomatic

(idiomatic, followed by a clause) Thinking or making assumptions, often incorrectly.

Japanese Meaning

～だと思い込む / ～だと考えている / ～だという誤った認識を持つ

会議は9時に始まると思い込んでいたので、誰もいなかったときは驚きました。

Sense（1）

(idiomatic, followed by a clause) Thinking or making assumptions, often incorrectly.

We opened a store in Beijing under the impression that our product would be popular.