Über Rangbestimmungen im Bereich der Modulformen vom Gewicht 1 der rationalen Modulgruppe
It is a difficult task to determine the dimension of spaces of modular forms of weight one. In Theorem 1.13 of his treatise ''Modulfunktionen und quadratische Formen'' (1982; Zbl 0493.10033) the author gave a formula for the dimension of the orthogonal complement of the space of cusp forms in the space of all entire modular forms of weight one and a real multiplier system on canonical subgroups of the modular group. In the present paper he proves that the result remains valid for non-real multiplier systems and some specific congruence subgroups \(\Gamma_ 0(\ell)\).
dimension of spaces of modular forms of weight one
scientific article; zbMATH DE number 3884247