mfkohnenbasis

Function: mfkohnenbasis
Section: modular_forms
C-Name: mfkohnenbasis
Prototype: G
Help: mfkohnenbasis(mf): mf being a cuspidal space of half-integral weight
 k >= 3/2, gives a basis B of the Kohnen + space of mf as a matrix
 whose columns are the coefficients of B on the basis of mf.
Doc: \kbd{mf} being a cuspidal space of half-integral weight $k\ge3/2$
 with level $N$ and character $\chi$, gives a
 basis $B$ of the Kohnen $+$-space of \kbd{mf} as a matrix whose columns are
 the coefficients of $B$ on the basis of \kbd{mf}. The conductor of either
 $\chi$ or $\chi \cdot (-4/.)$ must divide $N/4$.
 \bprog
 ? mf = mfinit([36,5/2],1); K = mfkohnenbasis(mf); K~
 %1 =
 [-1 0 0 2 0 0]

 [ 0 0 0 0 1 0]
 ? (mfcoefs(mf,20) * K)~
 %4 =
 [0 -1 0 0 2 0 0 0  0 0 0 0 0 -6 0 0 8 0 0 0 0]

 [0  0 0 0 0 1 0 0 -2 0 0 0 0  0 0 0 0 1 0 0 2]

 ? mf = mfinit([40,3/2,8],1); mfkohnenbasis(mf)
  ***   at top-level: mfkohnenbasis(mf)
  ***                 ^-----------------
  *** mfkohnenbasis: incorrect type in mfkohnenbasis [incorrect CHI] (t_VEC).
 @eprog In the final example both $\chi = (8/.)$ and $\chi \cdot (-4/.)$
 have conductor $8$, which does not divide N/4 = 10.