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

Eigenvarieties for non-cuspidal modular forms over certain PEL Shimura varieties