I have a game where the players have gotten an artifact (and went to a lot of trouble to get it). One NPC that was with them did have something negative happen to them (not major in the long term - the NPC is fine now and they know it).

They have not tried to investigate it at all. [One player has Identify which would give them some information.] They have kept it hidden (which *is* a good idea). They have an idea that it affects memories.

They have entered a part of the campaign where even a minimal knowledge of the artifact would be helpful, if not very important.

I don't know how to "suggest" to them that they investigate it without being heavy-handed. They haven't forgotten that they have it. They just seem to be unwilling to interact with it in any way. One player is very experienced, one has played before and another is relatively new. Two new players (very experienced) don't know about the artifact because the others keep it hidden.

Does anyone have any suggestions? If one of the NPCs (that they are about to encounter) knew they had it, they would be able to suggest investigating it. But they're keeping it very hidden.

This artifact is important to the campaign in the long run.  I'm beginning to think that I'll need to be heavy-handed with them... but would like to find another way.

Is this artifact well known in the world?  Would it make sense for them to come across information that would pique their curiosity?  They could find a letter which makes reference to something which matches its description (with or without naming the item) or hear a rumor somewhere that someone is looking for it, etc. 

You could have an assassination attempt and the would-be assassins have something linking them to the artifact (could be an item or article of clothing bearing the mark of someone who lost the artifact or is seeking it, or a "target" document describing the artifact and also describing the party at the time they obtained the artifact).

Or could the person carrying the artifact begin to notice some kind of effect, which might prompt them to investigate the cause?

Also: Have they been given reason to fear the artifact?  If their first interactions with it produced negative effects, they might simply be too fearful to mess with it, without a clear reason to do so.  Maybe they think the artifact was mostly a maguffin for one of the story arcs, and the important work related to it is already done (protecting it, keeping it out of the hands of the BBEG, keeping it from being unleashed on the world, etc. depending on what it is).  In that case you might have to give them a more urgent reason to investigate it.

For a more specific response, I would say a little more information about the nature of the artifact and its place in the world would be helpful.

Quote from tdouglas >>

 They have an idea that it affects memories.

I think this is your solution right here. If it has some effect on the PCs just by having it on them, then I think you can start dropping subtle nudges here and there. You could text/give a note to that player if you want to keep it private or just say to the table that this PC suddenly can't remember something or maybe they have a new memory of a place they've never been, etc...

Similar to what BK said, there are a number of ways you can have the artifact affect the players, or you could have some external encounters hint at something as well. Which ever way you go I think depends on the specifics of the artifact and how the PCs are interacting with it.

I can understand your concern as the DM who has the idea how everything should be working out and how the artifact relates. But, honestly, the players seem to be respectfully uneasy with the artifact which is actually surprisingly refreshing from their standpoint. I don't see a real problem at the moment. They know they have it... they know it's powerful... at some point using it appears to be incredibly necessary from your perspective and (maybe?) they can already predict that, but they just don't know when. I don’t see a problem with how they are choosing to be wilfully ignorant at this point, because that's their choice to make. The chips and dice can then fall as they were within the greater story narrative, being in a tight, hopeless spot and they choose to try to wield this unknown artifact in one last desparate move not knowing for sure what's going to happen. Very dramatic and enthralling.

If you'd prefer they know more in advance, the overt suggestions of assassins above is a good one, but I think very subtle mysterious hints can also be incredibly fun. Like, cryptic dream sequences the entire party shares together one night would prove it's not just one character's imagination, the artifact slightly glowing/humming under certain situations, more and more pronounced or unmistakable as days or weeks pass by. Small voices singing behind the ear, feeling the brush of warmth on the arm closest to the artifact. Basically, make it to a point so it can't be ignored, and curiosity will eventually take over for at least character (even if they aren't sure of the safety of doing so)

A powerful artifact would be a big target for thieves. If someone finds out that these characters have such an artifact, then the party may find themselves the victims of persistent attempts at pickpocketing, burglary, and even outright assault as every thief in the countryside tries to score a powerful artifact for themselves. Eventually the players will figure out that if so many people are so intent on acquiring this *thing*, then it must have some special significance. 

That's my 2 c.p.

Ordinary NPCs might not know they have it, but there are always powerful PCs that can know. They could have find out about it using a spell: Arcane Eye, Clairvoyance, and Scrying let the NPC see them with the artifact when they think no one is looking. Detect Magic or Locate Object may tell them when the object is near. Divination or Legend Lore may give them some hints about who has the object.

Or have the artifact become a problem. Like it's counting down to explode in 48 hours. They have to figure out how to stop it. Or it transforms a member of the party into a kuo-toa and they have to figure out how to reverse it.

Thank you for the suggestions everyone. I'm not sure I can go with assassins  but I have a powerful NPC (they have met once) that I might be able to use to encourage them to investigate it more. They could really use the simplest level of its powers right now. [The highest is very powerful and very, very dangerous to use.]

I like Bards.  So it should be no surprise that I would throw in a Bard's song that alludes to some ancient powerful artifacts.  The song would go so far as to mention that artifacts left alone can still be a problem, so it is better to know the devil you have than not know.  The Bard's song doesn't even have to be about The Artifact the party is carrying; it just needs to nudge them to find out what could happen if the thing were used against them.

Another method of getting the party some tiny information is to have a wizard and his friends come to the same place (tavern).  The wizard has a book with the same rune as the box/cloth covering/or whatever that the artifact was found.  The rune could simply be the school of magic that is connected to the artifact's powers.  Usually the party's curiosity will lead them to find out what the rune represents, and maybe more.

Another hook could be that the artifact gives off a sensation to the wizard because his book contains the same school of magic and the artifact "feels it."  The wizard asks who the owner of the cart is (assuming the artifact is being toted around in a cart) and he asks what they are carrying.  When they ask why he is asking or evades the questions, the wizard says he "knows" it is very powerful, and holds up his spell book to show them the rune.

The problem with the wizard method is the party may perceive this as some sort of threat and attack the wizard and his friends.  They may also become paranoid thinking the wizard won't let it go and is following them.  And maybe he is ...