Geodesic
Shimura integrals of cusp forms
Izvestiya. Mathematics , Tome 16 (1981) no. 3, pp. 603-646.

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This paper studies integrals of the form $\int_\alpha^{i\infty}\Phi z^k\,dz$ on the upper half-plane, where $\alpha$ is a rational number, $0\leqslant k\leqslant w$ is integral, and $\Phi$ is a cusp form of weight $w+2$ with respect to some modular group $\Gamma\subset\mathrm{SL}(2,\mathbf Z)$. The main result is that if $\Gamma$ is a congruence subgroup and $\Phi$ is an eigenvector of all the Hecke operators, then all these integrals are representable as linear combinations of two complex numbers with coefficients in some field of algebraic numbers. Bibliography: 13 titles. 
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V. V. Shokurov. Shimura integrals of cusp forms. Izvestiya. Mathematics , Tome 16 (1981) no. 3, pp. 603-646. http://geodesic.mathdoc.fr/item/IM2_1981_16_3_a5/

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