OFFSET
1,5
LINKS
FORMULA
Expansion of eta(q)^2*eta(q^11)^2 + 3*eta(q)*eta(q^3)*eta(q^11)*eta(q^33) + 3*eta(q^3)^2*eta(q^33)^2 in powers of q.
G.f. is a period 1 Fourier series which satisfies f(-1 / (33 t)) = 33 (t/i)^2 f(t) where q = exp(2 Pi i t).
EXAMPLE
G.f. = x + x^2 - x^3 - x^4 - 2*x^5 - x^6 + 4*x^7 - 3*x^8 + x^9 + ...
PROG
(PARI) {a(n) = if( n<1, 0, ellak( ellinit( [1, 1, 0, -11, 0], 1), n))};
(PARI) {a(n) = my(A, t1, t3); if( n<1, 0, n--; A = x * O(x^n); t1 = eta(x + A) * eta(x^11 + A); t3 = x * eta(x^3 + A) * eta(x^33 + A); polcoeff( t1^2 + 3*t1*t3 + 3*t3^2, n))};
(Magma) A := Basis( ModularForms( Gamma0(33), 2), 75); A[2] + A[3] - A[4] - A[5] - A[6];
(Sage)
def a(n):
return EllipticCurve("33a1").an(n) # Robin Visser, Sep 30 2023
CROSSREFS
KEYWORD
sign,mult
AUTHOR
Michael Somos, Feb 23 2020
STATUS
approved