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Atkin (1967) on page 22, equation (30), defines phi(tau) = eta(121*tau) / eta(tau), a modular function which satisfies phi(-1/(121*t)) = 11^(-1)/phi(t), where q = exp(2*Pi*i*t). On page 23, equation (33), he defines L_1(tau) = U phi(tau), where U is a Hecke operator so that the n-th Fourier coefficient of L_1 is the 11*n-th Fourier coefficient of phi. On page 26 , he finds that L_1(tau) = 11g_11*g_2(tau) + 2*11^2*g_3(tau) + 11^3*g_4(tau) + 11^4*g_5(tau), where g_2, g_3, g_4, g_5 are functions he previously defined. The n-th Fourier coefficient of L_1 is 11*a(n).

Atkin (1967) on page 22 , equation (30) , defines phi(tau) = eta(121*tau) / eta(tau), a modular function which satisfies phi(-1 / (121 *t)) = 11^(-1) / phi(t) , where q = exp(2 *Pi *i *t). On page 23 , equation (33) , he defines L_1(tau) = U phi(tau) , where U is a Hecke operator so that the n-th Fourier coefficient of L_1 is the 11*n-th Fourier coefficient of phi. On page 26 he finds that L_1(tau) = 11g_2(tau) + 2*11^2g_2*g_3(tau) + 11^3g_3*g_4(tau) + 11^4g_4*g_5(tau) , where g_2, g_3, g_4, g_5 are functions he previously defined. The n-th Fourier coefficient of L_1 is 11*a(n).

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A. O. L. Atkin, Proof of a conjecture of Ramanujan, Glasgow Math. J., 8 (1967), 14-32.

A. O. L. Atkin, <a href="https://doi.org/10.1017/S0017089500000045">Proof of a conjecture of Ramanujan</a>, Glasgow Math. J., 8 (1967), 14-32.

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G. C. Greubel, <a href="/A182668/b182668.txt">Table of n, a(n) for n = 1..1000</a>

eta[q_] := q^(1/24)*QPochhammer[q]; CoefficientList[Series[ eta[q^121]/ eta[q]/11, {q, 0, 300}], q][[1 ;; -1 ;; 11]] (* G. C. Greubel, Aug 10 2018 *)

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