Ring dimension and security level

I have some difficulties to understand how security level and ring dimension interact.
In my code I set the security level to 128bit classic and got a ring dimension of 2^17.
Then, I changed it to 192 and 256bit. I expected a higher ring dimension because it should be more difficult to decrypt these data but it stays at 2^17.
Is this the intended behavior and if so, could you explain it to me?