  Let $p$ be a prime number. Mazur proved that a geometrically maximal
unramified abelian covering of $X_0(p)$ over $\mathbb Q$ is given by the
Shimura covering $X_2(p) \to X_0(p)$, that is, a unique subcovering of $X_1(p)
\to X_0(p)$ of degree $N_p := (p-1)/\gcd(p-1, 12)$. In this short paper, we
show that a geometrically maximal abelian covering $X_2'(p) \to X_0(p)$ of
$X_0(p)$ over $\mathbb Q$ unramified outside cusps is cyclic of degree $2N_p$.
The main ingredient for the construction of $X_2'(p)$ is the generalized
Dedelind eta functions.
