  Generalising the recent method of Andreatta, Iovita, and Pilloni for cuspidal
forms, we construct an eigenvariety for symplectic and unitary groups that
parametrises systems of eigenvalues of overconvergent and locally analytic
$p$-adic automorphic forms. This is achieved by gluing some intermediates
eigenvarieties of a fixed 'degree of cuspidality'. The dimension of these
eigenvarieties is explicit and depends on the degree of cuspidality, it is
maximal for cuspidal forms and it is $1$ for forms that are 'not cuspidal at
all'. Under mild assumption, we are able to prove a conjecture of Urban about
the dimension of the irreducible components of Hansen's eigenvariety in the
case of the group $\mathrm{GSp}_4$ over $\mathbb{Q}$.

Number Theory