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# Conductor of monomial forms withtrivialnebentypus

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How does one see

Is it true that the conductor of a monomial form cannot be square-free? I am specifically interested in forms of holomoprhic or a Maass ' type associated cusp form with real quadratic fields.trivial nebentypus corresponding to a two-dimensional dihedral representation (over $\mathbb{Q}$ )is non-square-free?

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# Conductor of monomial formforms

How does one see that the conductor of a monomial form cannot be square-free? I am specifically interested in forms of Maass' type associated with real quadratic fields.