Function: mftwist
Section: modular_forms
C-Name: mftwist
Prototype: GG
Help: mftwist(F,D): returns the twist of the form F by the
integer D, i.e., the form G such that mfcoef(G,n)=(D/n)mfcoef(F,n),
where (D/n) is the Kronecker symbol.
Doc: $F$ being a generalized modular form, returns the twist of $F$ by the
integer $D$, i.e., the form $G$ such that
\kbd{mfcoef(G,n)=}$(D/n)$\kbd{mfcoef(F,n)}, where $(D/n)$ is the Kronecker
symbol.
\bprog
? mf = mfinit([11,2],0); F = mfbasis(mf)[1]; mfcoefs(F, 5)
%1 = [0, 1, -2, -1, 2, 1]
? G = mftwist(F,-3); mfcoefs(G, 5)
%2 = [0, 1, 2, 0, 2, -1]
? mf2 = mfinit([99,2],0); mftobasis(mf2, G)
%3 = [1/3, 0, 1/3, 0]~
@eprog\noindent Note that twisting multiplies the level by $D^2$. In
particular it is not an involution:
\bprog
? H = mftwist(G,-3); mfcoefs(H, 5)
%4 = [0, 1, -2, 0, 2, 1]
? mfparams(G)
%5 = [99, 2, 1, y]
@eprog