I have a two week old crown. There a visible black line where it meets the gum. Should I be worried?

You have what is called a porcelain fused to metal (PFM) crown.  Many times these will show a black line at the top.  This is just the metal that is exposed.  To prevent this we use all porcelain crowns.  There are several advantages to metal free crowns:1.  Stronger bond strength and many    times a better marginal seal due to the cement that is used.2.  More aesthetic as there is no black line showing.3.  Can see through them on an X-ray making future problems with the tooth (recurrent decay, etc) easier to diagnose.  4.  Typically,  gum tissues are much healthier around an all porcelain crown as compared to a PFM crown.  

Normally we try to hide the margin of a crown just below the edge of the tissue.  With a PFM crown the gray of the metal underneath the porcelain may appear as a black line at the tissue if the margin of the crown was not placed properly.  Many times this happens over the years if your tissue receeds.  Otherwise the crown may be sealed, but the bleeding might be someting to be checked out by your dentist and you can ask about your concerns about the black line at that time also.

A visible black line does not mean something is wrong with the tooth or the crown. Metal is sometimes used under the porcelain of a crown to make the crown stronger. You may be seeing a thin line of this metal showing. Another factor can be a dark root. If the root of the tooth is dark then a small amount of the root that is not covered by the crown may appear as a dark line. If there is indeed an opening between the tooth and the crown this should be evaluated by the dentist who placed the crown. If there is nothing wrong with the tooth or the crown then you will have to determine if it is enough of a cosmetic problem that you would want to replace the crown for a better look. 

Without a picture (I have none now) I can only generalize.  Worried?  About looks or about fit?  Porcelain fused to metal construction often has that cast, and if it is not an esthetic issue, no big deal.  They are good crowns.  Sometime the prosthetic crown is a lighter color than the tooth root, so what seems to be a line is really just your tooth's darker enamel or root showing  (the dentist may have opted NOT to cover below the gums to avoid hypersensitivity).  If the line comes from a significant gap between the crown and the tooth, that could be an ill-fitting crown and your dentist will want to know about that right away.