  In this paper, we give a method to construct a classical modular form from a
Hilbert modular form. By applying this method, we can get linear formulas which
relate the Fourier coefficients of the Hilbert and classical modular forms. The
paper focuses on the Hilbert modular forms over real quadratic fields. We will
state a construction of relations between the special values of L-functions,
especially at $0,$ and arithmetic functions. We will also give a relation
between the sum of squares functions with underlying fields
$\mathbb{Q}(\sqrt{D})$ and $\mathbb{Q}$.

Number Theory