Which PARI-commands evaluates the q-expansion, i.e. the Fourier coefficents of the modular j-invariant?
Note. ellj(x) computes single values of j; and mfcoefs(-,-) computes coefficents. But mfcoefs(ellj,8) is not accepted.
2026-03-27 00:59:55.1774573195
Evaluating in PARI/GP the Fourier coefficients of the j -invariant?
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I learned: PARI expects the function as defined by its mapping rule
F = x -> ellj(x);
V = laurentseries(F,8);
print("q-expansion of modular j-invariant: ", V);
Output:
q-expansion of modular j-invariant: x^-1 + 744 + 196884x + 21493760x^2 + 864299970x^3 + 20245856256x^4 + 333202640600x^5 + 4252023300096x^6 + 44656994071935x^7 + 401490886656000x^8 + O(x^9)