What are the model parameters in PCA?
From an algebra point of view PCA is a base change. You can write the transformation as:
$$ T = XW $$
Where $X$ is an nxp matrix (n instance, p features) and $W$ is a pxp 'weight' matrix (whose columns are eigenvectors of $X^TX$ - translating one base to another). Hence the general PCA has $p^2$ coefficients.
You can also reduce the space to m dimensions and use :
$$ T = XW_m $$
Where $W_m$ is a weight matrix constituted of m first columns of $W$. $W_m$ is a pxm weight matrix and has pxm coefficients (or easier to understand : mxp coefficients, that is number of dimension kept and parameters needed to express the new base vector in terms of the initial base). In the case of a projection onto 2 dimensions you will have 2p coefficients.