Generally, YES if it belongs to the employer (which it usually does), otherwise not. But, further details are needed to decide, and are outlined below.
In What Capacity Did You Work For The Prior Employer?
If you worked in a highly technical capacity where there was lots of proprietary material, you have a higher duty that may last a long, long time, perhaps as long as the trade secrets involved are secret and have commercial value. On the other hand if you were a mail clerk, janitor or common laborer you likely have few trade secrets.
How Long Did You Work There?
The longer you worked, the more reasonable to expect you to keep trade secrets and the more a Judge is likely to think you have valuable trade secrets. I used to work in the R&D Department as IP Attorney for Winchester (yes, that Winchester - as in guns & ammo & hunting stuff) 20 years ago, and I am likely still restricted on certain trade secrets.
Did you sign a confidentiality agreement or employment agreement obligating you to secrecy?
Almost every major employer has employees sign an "Employee Agreement" prepared by an attorney, usually an IP attorney, requiring you to assign inventions and keep trade secrets. If you signed one, your risk of disclosing such secrets is significant.
Is it imperative for you to disclose trade secrets to show your work to get another job?
It is almost always not imperative and not wise for you to disclose your previous employer's trade secrets. In fact, disclosing substrate secrets is usually unwise when job interviewing as it tells your prospective employer that you are disloyal and cannot be trusted with their trade secrets. In 20 years as a corporate lawyer, I turned down every single candidate that proposed to disclose or use their previous employer's trade secrets. I wanted an employee I could trust not one that was cheating on their previous employer. In fact, it was much more attractive to me when a job applicant said he or she could not ethically disclose trade secrets of a previous employer. Please keep that in mind.
Have you asked permission?
If you haven't, you are at risk.
You can't afford this fight, as it will likely make and keep you unemployed.
Absolutely you should not be fighting that fight if you can settle it by agreeing that you will not disclose any trade secrets and removing any thing they say is a trade secret from whatever they want you to remove it from. You might time this negative problem into a positive if you immediately comply and promise never to reveal any secrets ever again. Perhaps that would turn a negative job reference into a neutral or even positive one.