1Function: mfatkin 2Section: modular_forms 3C-Name: mfatkin 4Prototype: GG 5Help: mfatkin(mfatk,f): Given an mfatk output by mfatk = mfatkininit(mf,Q) 6 and a modular form f belonging to the space mf, returns the modular form 7 g = C*f|W_Q where C = mfatk[3] is a normalizing constant so that g 8 has the same field of coefficients as f; mfatk[1] = mf2 (or 0 if mf2=mf) 9 which is the space to which g belongs. 10Doc: Given a \kbd{mfatk} output by \kbd{mfatk = mfatkininit(mf,Q)} and 11 a modular form $f$ belonging to the pace \kbd{mf}, returns the modular 12 form $g = C \times f|W_Q$, where $C = \kbd{mfatk[3]}$ is a normalizing 13 constant such that $g$ has the same field of coefficients as $f$; 14 \kbd{mfatk[3]} gives the constant $C$, and \kbd{mfatk[1]} gives 15 the modular form space to which $g$ belongs (or is set to $0$ if 16 it is \kbd{mf}). 17 \bprog 18 ? mf = mfinit([35,2],0); [f] = mfbasis(mf); 19 ? mfcoefs(f, 4) 20 %2 = [0, 3, -1, 0, 3] 21 ? mfatk = mfatkininit(mf,7); 22 ? g = mfatkin(mfatk, f); mfcoefs(g, 4) 23 %4 = [0, 1, -1, -2, 7] 24 ? mfatk = mfatkininit(mf,35); 25 ? g = mfatkin(mfatk, f); mfcoefs(g, 4) 26 %6 = [0, -3, 1, 0, -3] 27 @eprog 28