On generation of the coefficient field of a primitive Hilbert modular form by a single Fourier coefficient

Narasimha Kumar, Satyabrat Sahoo

For a primitive Hilbert modular form $f$ over $F$ of weight $k$, under certain assumptions on image of ${\bar{\rho }}_{f,\lambda }$, we calculate the Dirichlet density of primes $\mathfrak{p}$ fo…