Let V be a nonzero subspace of the complex vector space \( M_6(\mathbb{C}) \) such that every nonzero matrix in V has eigenvalues with nonzero imaginary parts. Determine the possible dimension of V over \(\mathbb{C} \).
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Let V be a nonzero subspace of the complex vector space \( M_6(\mathbb{C}) \) such that every nonzero matrix in V has eigenvalues with nonzero imaginary parts. Determine the possible dimension of V over \(\mathbb{C} \).