Is it acceptable to follow up on an interview after the thank you letter/email?

Basically subject, but for a little more context.

I had an interview for a job that I am very excited about- and it is almost as perfect as perfect can be.one or two business days after the interview (per advice of a few websites via google search) I sent a brief thank you email expressing thanks/ interest in continuing the process/mission/etc It was brief though..

During the interview, I forget the exact phrase he used, but a timeline of "two to four weeks" was expressed.

This thursday will represent the two week mark.

Given that I have already sent a thank you email, AND it has been two weeks- Is it acceptable to send another email with the goal of essentially.. "Have you had the opportunity to give our conversation any thought//reached a decision//remember me?"

If it is acceptable, what would a safe/general template look like?

Edit: This is for a first fresh out of college or career change job.

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