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In his papers [7] and [10], Hecke proved that every L-function with a Hecke character of an imaginary quadratic field is obtained as the Mellin transformation of a cusp form with respect to a certain congruence subgroup of SL2(Z). For a fixed congruence subgroup P of SL2(Z), we obtain, from a cusp form f of weight 2 with respect to F, a holomorphic 1-form f (z)dz (z E) on the compactification (5~/P)* of c I/P (the quotient of the complex upper half

On abelian varieties with complex multiplication as factors of the abelian variety attached to Hilbert modular forms