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