FUNCTION : ETA[UpLB] - lower bound for ord(Up(EP),r) CALLING SEQUENCE : UpLB() UpLB(EP,r,N1,p) PARAMETERS : EP - etaproduct r - rational N1 - positive integer divisible by prime p p - prime GLOBAL VARIABLES : SYNOPSIS : EP assumed to be a modular function on level divisible by p^2 Let N = N1/p (if p^2|N1) otherwise N = N1 So if EP is MF on GAMMA0(N1) then Up(EP) is MF on GAMMA0(N) This function returns a lower bound for ord(Up(EP),r) where r is a cusp of Up(EP). EXAMPLES : DISCUSSION : SEE ALSO :