1,2

Coefficients of level 11 weight 2 cusp form with trivial character.

Barry Cipra, What's Happening in the Mathematical Sciences, Vol. 5, Amer. Math. Soc., 2002; see p. 5.

H. Darmon, A proof of the full Shimura-Taniyama-Weil conjecture is announced, Notices Amer. Math. Soc., Dec. 1999, pp. 1397-1401.

F. Diamond, Congruences between modular forms: raising the level and dropping Euler factors, in Elliptic curves and modular forms (Washington, DC, 1996). Proc. Nat. Acad. Sci. U.S.A. 94 (1997), 11143-11146.

N. D. Elkies, Elliptic and modular curves..., in AMS/IP Studies in Advanced Math., 7 (1998), 21-76, esp. p. 42.

Shimura, Goro; A reciprocity law in non-solvable extensions. J. Reine Angew. Math. 221 1966 209-220.

J. H. Silverman, A Friendly Introduction to Number Theory, 3rd ed., Pearson Education, Inc, 2006, p. 412.

A. Wiles, Modular forms, elliptic curves and Fermat's last theorem, pp. 243-245 of Proc. Intern. Congr. Math. (Zurich), Vol. 1, 1994.

T. D. Noe, Table of n, a(n) for n=1..1002

J. Cowles, Some congruence properties of three well-known sequences: Two notes, J. Num. Theory 12(1) (1980) 84.

W. A. Stein, The Modular Forms Database

a(n) is multiplicative with a(11^e) = 1, a(p^e) = a(p)*a(p^(e-1)) - p*a(p^(e-2)) for p != 11. - Michael Somos Feb 12 2006

a(n) = A000594(n) (mod 11). [Cowles]. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 13 2007

Expansion of (eta(q)* eta(q^11))^2 in powers of q.

Euler transform of period 11 sequence [ -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -4, ...] . - Michael Somos Feb 12 2006

G.f. A(x) satisfies 0= f(A(x), A(x^2), A(x^4)) where f(u, v, w)= u*w*(u+ 4*v+ 4*w)- v^3 . - Michael Somos Mar 21 2005

G.f. is a period 1 Fourier series which satisfies f(-1 / (11 t)) = 11 (t/i)^2 f(t) where q = exp(2 pi i t).

Coefficients of L-series for elliptic curve "11a3": y^2 + y = x^3 - x^2 . - Michael Somos May 23 2008

q - 2*q^2 - q^3 + 2*q^4 + q^5 + 2*q^6 - 2*q^7 - 2*q^9 - 2*q^10 + ...

(MAGMA) [ Coefficient(Basis(ModularForms(Gamma0(11), 2))[2], n) : n in [1..100] ]; /* Klaus Brockhaus, Jan 31 2007 */

(PARI) {a(n)=local(A, p, e, x, y, a0, a1); if(n<1, 0, A=factor(n); prod(k=1, matsize(A)[1], if(p=A[k, 1], e=A[k, 2]; if(p==11, 1, a0=1; a1=y=-sum(x=0, p-1, kronecker(4*x^3-4*x^2+1, p)); for(i=2, e, x=y*a1-p*a0; a0=a1; a1=x); a1))))} /* Michael Somos Aug 13 2006 */

(PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( (eta(x + A) * eta(x^11 + A))^2, n))}

(MAGMA) [ Coefficient(qEigenform(EllipticCurve([0, -1, 1, 0, 0]), n+1), n) : n in [1..100] ]; /* Klaus Brockhaus, Jan 29 2007 */

(PARI) {a(n) = ellak( ellinit( [0, -1, 1, 0, 0], 1), n)}

Cf. A002070 (terms with prime indices). Convolution square of A030200.

Sequence in context: A124333 A002107 A133099 this_sequence A094781 A023582 A023518

Adjacent sequences: A006568 A006569 A006570 this_sequence A006572 A006573 A006574

sign,easy,nice,mult

njas