Hash Table: Relation between position of a value and Hash table size
No.  If you use SHA512, you can use any modulus $S$ you want: it doesn't need to be prime.  A power of two is fine and is no better or worse than a prime.

The reason is that the cryptographic properties of SHA512 ensure that the output of SHA512 is (for all practical purposes) essentially a uniformly random 512-bit string.  Because $2^{512}$ is so much larger than your modulus, after reducing modulo $S$, the result will be approximately uniform.  Any non-uniformity will be incredibly, exponentially small: so small that it's not detectable within your lifetime, or the lifetime of the solar system.  (I know there's another answer that claims non-uniformity is a problem, but that answer failed to quantify the extent of the non-uniformity and thus came to the wrong conclusion; the amount of non-uniformity is so exponentially small that it's completely irrelevant in practice).

So, go ahead and use any modulus that's convenient.  It doesn't need to be a power of two or a prime number, if you're using SHA512 as your hash function.