Function: mfsturm
Section: modular_forms
C-Name: mfsturm
Prototype: lG
Help: mfsturm(NK): Sturm bound for modular forms on G_0(N) and
 weight k, i.e., an upper bound for the order of the zero at infinity of
 a nonzero form. NK is either [N,k] or an mfinit (exact bound in the
 latter case).
Doc: Gives the Sturm bound for modular forms on $\Gamma_{0}(N)$ and
 weight $k$, i.e., an upper bound for the order of the zero at infinity of
 a nonzero form. \kbd{NK} is either

 \item a pair $[N,k]$, in which case the bound is the floor of $(kN/12) \cdot \prod_{p\mid N} (1+1/p)$;

 \item or the output of \tet{mfinit} in which case the exact upper bound is returned.

 \bprog
 ? NK = [96,6]; mfsturm(NK)
 %1 = 97
 ? mf=mfinit(NK,1); mfsturm(mf)
 %2 = 76
 ? mfdim(NK,0) \\ new space
 %3 = 72
 @eprog
