  Borisov and Gunnells observed in 2001 that certain linear relations between
products of two holomorphic weight 1 Eisenstein series had the same structure
as the relations between periods of modular forms; a similar phenomenon exists
in higher weights. We give a conceptual reason for this observation in
arbitrary weight. This involves an unconventional way of expanding the
Rankin-Selberg convolution of a cusp form with an Eisenstein series. We also
prove a partial result towards understanding the action of a Hecke operator on
a product of two Eisenstein series.
