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An explicit dimension formula for the spaces of generalized automorphic forms with respect to $\mathrm{Sp}\left( {2,\mathbf{Z}} \right)$

An explicit dimension formula for the spaces of generalized automorphic forms with respect to $\mathrm{Sp}\left( {2,\mathbf{Z}} \right)$

Let be the Siegel upper half plane of degree g.The real sym- plectic group Sp(g, R) acts on as Z M. Z =(AZ + B)(CZ + D) -1, Jor (A B) e Sp (g, R)