FUNCTION :  Gamma1ModFunc - Checks whether the generalized eta-quotient
                            corresponding to the geta-list L is a
                            modular function of Gamma[1](N)

CALLING SEQUENCE :  Gamma1ModFunc(L,N)

PARAMETERS :      L - (geta)-list produced by GETAP2getalist
                      and corresponds to a generalized eta-quotient
                      on Gamma[1](N).
                  N - positive integer

GLOBAL VARIABLES : xprint (default=false)

SYNOPSIS :   Checks whether the generalized eta-quotient
             corresponding to the geta-list L is a modular function 
             of Gamma[1](N). It returns 1 if it is a modular function
             otherwise it returns 0. It also prints diagnostics.
             This function is needed in the proc provemodfuncid.

             If xprint is true then extra info is printed.

EXAMPLES :   

> with(thetaids):

> Gamma1ModFunc();
-------------------------------------------------------------
Gamma1ModFunc(L,N)                                               
   L is a getalist; i.e. L=[[b1,a1,c1],....]
   and assumes each a1, a2, etc is not zero.
   Let G be the corresponding generalized eta-function.
   Checks whether G is a modular function of Gamma[1](N).
   Returns 1 if it is a modular function otherwise 0.
   It also prints diagnostics.
-------------------------------------------------------------

> eprod := GETA(40,3)^2/GETA(40,4)^5*GETA(40,5)^4/GETA(40,6)^3
           *GETA(40,7)^2*GETA(40,8)^2/GETA(40,10)^2*GETA(40,13)^2
           /GETA(40,14)^3*GETA(40,15)^4/GETA(40,16)^4*GETA(40,17)^2
           /GETA(40,20)/GETA(20,1)^2*GETA(20,2)^3/GETA(20,3)^2
           *GETA(20,4)*GETA(20,6)^3/GETA(20,7)^2*GETA(20,8)
           /GETA(20,9)^2;

> L2:=GETAP2getalist(eprod);
L2 := [[40, 3, 2], [40, 4, -5], [40, 5, 4], [40, 6, -3], [40, 7, 2],
    [40, 8, 2], [40, 10, -2], [40, 13, 2], [40, 14, -3], [40, 15, 4],
    [40, 16, -4], [40, 17, 2], [40, 20, -1], [20, 1, -2], [20, 2, 3],
    [20, 3, -2], [20, 4, 1], [20, 6, 3], [20, 7, -2], [20, 8, 1],
    [20, 9, -2]]
> Gamma1ModFunc(L2,40);    
                                       1

> xprint:=true:
> Gamma1ModFunc(L2,40);    
* starting Gamma1ModFunc with L=[[40, 3, 2], [40, 4, -5], [40, 5, 4], 
  [40, 6, -3], [40, 7, 2], [40, 8, 2], [40, 10, -2], [40, 13, 2], 
  [40, 14, -3], [40, 15, 4], [40, 16, -4], [40, 17, 2], [40, 20, -1], 
  [20, 1, -2], [20, 2, 3], [20, 3, -2], [20, 4, 1], [20, 6, 3], [20, 7, -2], 
  [20, 8, 1], [20, 9, -2]] and N=40 
All n are divisors of 40
val0=0
which is even.
valinf=2
which is even.
It IS a modfunc on Gamma1(40)

DISCUSSION : We see that the generalized eta-quotient eprod is
             a Modular Function on Gamma[1](40).

SEE ALSO :  2getalist, 
provemodfuncid