Ramanujan's tau function is represented by an infinite family of convolution sums of twisted divisor functions obtained by explicitly constructing non-vanishing level-1 cusp forms from higher-level modular forms.
Maass operators and van der Pol-type identities for Ramanujan’s tau function.Acta Arith., 113(2):157–167
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Representation of Ramanujan's tau function by twisted divisor functions
Ramanujan's tau function is represented by an infinite family of convolution sums of twisted divisor functions obtained by explicitly constructing non-vanishing level-1 cusp forms from higher-level modular forms.