  We describe an algebra of meromorphic functions on the Siegel domain of genus
two which contains Siegel modular forms for an arithmetic index six subgroup of
the symplectic group and it is closed under three canonical derivations of the
Siegel domain. The main ingredients of our study are the moduli of enhanced
genus two curves, Gauss-Manin connection and the modular vector fields living
on such moduli spaces.
