Hilbert's irreducibility, modular forms, and computation of certain Galois groups (Q6046939)

In this work, the authors consider Hilbert's irreducibility, modular forms and computation of certain Galois groups. They discuss previous work: [\textit{I. Kodrnja}, Monatsh. Math. 186, No. 4, 653--661 (2018; Zbl 1436.11045); \textit{G. Muić}, Ramanujan J. 27, No. 2, 181--208 (2012; Zbl 1267.11040); Monatsh. Math. 173, No. 2, 239--256 (2014; Zbl 1307.11052); Monatsh. Math. 180, No. 3, 607--629 (2016; Zbl 1372.11057); with \textit{D. Mikoč} Glas. Mat., III. Ser. 48, No. 2, 301--312 (2013; Zbl 1328.14042)]. They study certain Galois groups and splitting fields of rational functions in \(\mathbb{Q}(X_{0}(N))\) using Hilbert's irreducibility theorem and modular forms. They derive their results using MAGMA and SAGE.