I heard the new crown crack while being installed.

Can you SEE the crack, or was it merely a sensation?  I only ask because I had a pt email that their brand new veneers were not good, that there were gaps at the gum-line and stains.  When she got to the office, there were no stains, but one could see with a microscope (she used a magnifying glass) the faint outline of the slightly yellow color of her roots of 2 lower teeth (not stain) and there were no gaps or open margins, it was simply that the edge of the veneers were not below the gum-line so you could barely make out the .3 mm distance from veneer edge to gum-line.  No risk of decay, no stains, no open margin.So it is "possible" that what appears to you as abnormal is simply normal or designed by the lab for characterization.Or it is cracked and should be replaced.

Sounds like you need to get a new crown.  Things happen.  No one is perfect, but I do think that you will need a new crown.