How can I SHA512 a string in C#?

Your code is correct, but you should dispose of the SHA512Managed instance:

using (SHA512 shaM = new SHA512Managed())
{
   hash = shaM.ComputeHash(data);
}

512 bits are 64 bytes.

To convert a string to a byte array, you need to specify an encoding. UTF8 is okay if you want to create a hash code:

var data = Encoding.UTF8.GetBytes("text");    
using (...