I've seen people say that wavefunctions represented as vectors in a Hilbert space can (but don't have to) have infinite dimensions. So if a state vector requires X number of basis eigenfunctions linearly combined to represent it the state vector itself must have X components (dimensions)?
So in the case of momentum space, the total wavefunction is some linear combination of plane wave form eigenfunctions, if there are infinite eigenfunctions this is an infinite dimensional Hilbert space? Or if the wavefunction state vector required only 100 eigenfunctions to describe it, this state vector exists in a 100 dimensional Hilbert space?
Maybe I'm misunderstanding something fundamental, I'm still very new to this stuff. Thank you in advance for any answers.