I downloaded Lady Gaga's Artpop and when I go to download it, it says it is purchased but doesn't allow me to listen to it.

Hello Emily,

I am sure you are eager to listen to the new Lady Gaga album. I have a few suggestions to get it downloaded to your iPhone.

First, I recommend checking to see if the download was interrupted:

If your download was interrupted using your iPhone, iPad, or iPod touch

1. From the Home screen, tap the iTunes app.
2. For iPhone or iPod touch, tap More > Downloads. For iPad, tap Downloads.
3. Enter your account name and password if prompted.
4. Tap the blue download arrow to resume.

iTunes: How to resume interrupted iTunes Store downloads

http://support.apple.com/kb/ht1725

If the album still does not download, next I recommend downloading the album from your list of past purchases. Follow the steps in the section titled "iPhone, iPad, or iPod touch > Music" in the article below:

Downloading past purchases from the App Store, iBookstore, and iTunes Store

http://support.apple.com/kb/ht2519

If you are still not able to play the songs, you can report an issue with these purchases using the steps in this article:

How to report an issue with your iTunes Store, App Store, Mac App Store, or iBookstore purchase

http://support.apple.com/kb/ht1933

Best,

Sheila M.