A new proof of the Ramanujan congruences for the partition function (Q2426718)

Let \(p(n)\) denote the number of partitions of \(n\). Let \(\tau(n)\) be Ramanujan's \(\tau\) function. Ramanujan's congruences \[ p(5n+4) \equiv 0 \pmod 5, \] \[ p(7n+5) \equiv 0 \pmod 7, \] \[ p(11n+6) \equiv 0 \pmod{11} \] are equivalent to the congruences \(\tau(\ell n) \equiv 0 \pmod{\ell}\) for \(\ell = 5,7\), and \(11\). The authors show how the congruences for \(\tau(n)\) follow from a result of \textit{Y. Choie, W. Kohnen}, and \textit{K. Ono} [Bull. Lond. Math. Soc. 37, No. 3, 335--341 (2005; Zbl 1155.11325)) on the vanishing of the constant term of certain modular forms.