Function: mfperiodpol
Section: modular_forms
C-Name: mfperiodpol
Prototype: GGD0,L,b
Help: mfperiodpol(mf,f,{flag=0}): period polynomial of the cuspidal part of
the form f, in other words integral from 0 to ioo of (X-tau)^(k-2)f(tau).
If flag=0, ordinary period polynomial, if flag=1 or -1, even or odd
part of that polynomial. f can also be the modular symbol output by
mfsymbol(mf,f).
Doc: period polynomial of the cuspidal part of the form $f$, in other words
$\int_0^{i\infty}(X-\tau)^{k-2}f(\tau)\,d\tau$. If \kbd{flag} is $0$, ordinary
period polynomial. If it is $1$ or $-1$, even or odd part of that polynomial.
$f$ can also be the modular symbol output by \kbd{mfsymbol}(mf,f).
\bprog
? D = mfDelta(); mf = mfinit(D,0);
? PP = mfperiodpol(mf, D, -1); PP/=polcoeff(PP, 1); bestappr(PP)
%1 = x^9 - 25/4*x^7 + 21/2*x^5 - 25/4*x^3 + x
? PM = mfperiodpol(mf, D, 1); PM/=polcoeff(PM, 0); bestappr(PM)
%2 = -x^10 + 691/36*x^8 - 691/12*x^6 + 691/12*x^4 - 691/36*x^2 + 1
@eprog