Regarding modular forms

["LNU, Swati" <S10@email.sc.edu>]

Hello,

I am trying to write a function in PARI/GP that takes as input a polynomial in Delta (Ramanujan Delta function) and a list L whose nth term is given by s(n) = {2 * D(1) * h(n - 4) + (2 * D(2) * h(n - 5)) + ((D(4) + (2 * D(1))) * h(n - 7)) + ((D(5) + D(2)) * h(n - 8)) + (2 * D(9) * h(n - 9));} where h(a) = {T(Del(a, 2000 - a, 3), 7, 12 * a, 3) - (2 * Del(a, 2000 - a, 3));}, D(n) = {Mod(Ser(mfcoefs(mfpow(mfDelta(), n), 100), q), 3);} and Del(a , n , m ) = q^a*(eta(Mod(1,m)*q+O(q^(n+1))))^(24*a); and outputs the minimal k such that T^k (f) = 0 modulo 3.

Here,  T (f , p , k , m ) = {    f = truncate ( f ) ;    sum ( n =0 , poldegree ( f ) \ p ,    sumdiv ( gcd (p , n ) , r , polcoeff (f , p * n / r ^2) * r^(k-1) ) * q ^ n) +    O ( q ^( poldegree ( f ) \ m + 1) ) ; }

Could someone help in this regard?

Thank you very much for your time.

Swati

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