I was going to suggest something like this until I saw Ruellit's message. I think it would be more effective if you did it with a time-delay.
It takes a long time to get acquainted with a site. If you record the date a new user signs up and send the offer of a free trial after they've been unable to use the premium features for a while, they'll have a clearer view of what they're missing.
The period from initial signup until the offer should be the earliest of (for example) the 25th visit or 30 days, or something like that.
The free trial should probably be presented with hand-holding (Have you seen THIS??) and the new member should be allowed to postpone the presentation for some period of time.
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