Function: mfatkin
Section: modular_forms
C-Name: mfatkin
Prototype: GG
Help: mfatkin(mfatk,f): Given an mfatk output by mfatk = mfatkininit(mf,Q)
 and a modular form f belonging to the space mf, returns the modular form
 g = C*f|W_Q where C = mfatk[3] is a normalizing constant so that g
 has the same field of coefficients as f; mfatk[1] = mf2 (or 0 if mf2=mf)
 which is the space to which g belongs.
Doc: Given a \kbd{mfatk} output by \kbd{mfatk = mfatkininit(mf,Q)} and
 a modular form $f$ belonging to the pace \kbd{mf}, returns the modular
 form $g = C \times f|W_{Q}$, where $C = \kbd{mfatk[3]}$ is a normalizing
 constant such that $g$ has the same field of coefficients as $f$;
 \kbd{mfatk[3]} gives the constant $C$, and \kbd{mfatk[1]} gives
 the modular form space to which $g$ belongs (or is set to $0$ if
 it is \kbd{mf}).
 \bprog
 ? mf = mfinit([35,2],0); [f] = mfbasis(mf);
 ? mfcoefs(f, 4)
 %2 = [0, 3, -1, 0, 3]
 ? mfatk = mfatkininit(mf,7);
 ? g = mfatkin(mfatk, f); mfcoefs(g, 4)
 %4 = [0, 1, -1, -2, 7]
 ? mfatk = mfatkininit(mf,35);
 ? g = mfatkin(mfatk, f); mfcoefs(g, 4)
 %6 = [0, -3, 1, 0, -3]
 @eprog
