Function: mfEH
Section: modular_forms
C-Name: mfEH
Prototype: G
Help: mfEH(k): k>0 being in 1/2+Z, mf corresponding to the Cohen-Eisenstein
 series H_k of weight k on G_0(4).
Doc: $k$ being in $1/2+\Z_{\geq 0}$, return the mf structure corresponding to
 the Cohen-Eisenstein series $H_{k}$ of weight $k$ on $\Gamma_{0}(4)$.
 \bprog
 ? H = mfEH(13/2); mfcoefs(H,4)
 %1 = [691/32760, -1/252, 0, 0, -2017/252]
 @eprog The coefficients of $H$ are given by the Cohen-Hurwitz function
 $H(k-1/2,N)$ and can be obtained for moderately large values of $N$ (the
 algorithm uses $\tilde{O}(N)$ time):
 \bprog
 ? mfcoef(H,10^5+1)
 time = 55 ms.
 %2 = -12514802881532791504208348
 ? mfcoef(H,10^7+1)
 time = 6,044 ms.
 %3 = -1251433416009877455212672599325104476
 @eprog
