Is it possible to diagonalize a matrix whose elements are given as functions of the indices without specifying the number of dimensions?

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I have been given a matrix whose elements are given by

$$({n^2\pi^2\over2a^2}+{a^2(n^2\pi^2-6)\over24\pi^2n^2})\delta_{mn}+{2a^2mn[1+(-1)^{m+n}]\over\pi^2(m-n)^2(m+n)^2}(1-\delta_{mn})$$

The matrix is square, but the number of dimensions is not given. I am told that the number of dimensions is given by a finite number N, and I am told to diagonalize the matrix. Is this diagonalization possible without knowing the value of N? If so, how can it be done?