= Fricke sign from a nonvanishing fixed-point value
{c}
{title2=$\tau_*=i/\sqrt N$}
If a one-dimensional <modular cusp> space is stable under the phase-normalized <Fricke involution>, its scalar action is determined by evaluation at the fixed point. The phase-normalized prefactor is one there; if the form is nonzero at that point, the <eigenvalue> is $+1$. A product with strictly positive convergent factors on the imaginary axis supplies such a value and also makes the central completed <L-function of a cusp form> positive when its central Mellin integral has real positive kernel.
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