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How many Hecke operators span the level 1 Hecke algebra?
$\Delta$ is the basis element $f_{12, -1}$ using the notation above, so by duality, Lehmer's conjecture is equivalent to the nonvanishing, for all positive $n$, of the coefficient of $q^{-1}$ in the weight $-10$ form $f_{-10, n} = q^{-n} + \tau(n) q^{-1} + \ldots$. Unfortunately, it doesn't seem to be easy to show that this is never zero. |
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answered | How many Hecke operators span the level 1 Hecke algebra? |