Suppose I have a matrix A from the modular group, whose eigenvalues are numbers from a suitable quadratic field $Q(\sqrt D)$, where D depends on the trace of the matrix. Is there a way to find the corresponding eigenvectors so their components would be quadratic integers from the same field? Is it possible always, never or just for some subset of the modular group?
2026-05-10 17:17:43.1778433463
Eigenvectors of PSL(2,Z) in terms of quadratic integers
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