Let p be a prime number. Mazur proved that a geometrically maximal unramified abelian covering of X(p) over Q is given by the Shimura covering X2(p) → X(p) , that is, a unique subcovering of X1(p) → X(p) of degree Np: = (p- 1) / gcd (p- 1 , 12). In this short paper, we show that a geometrically maximal abelian covering X2′(p)→X0(p) of X(p) over Q unramified outside cusps is cyclic of degree 2 Np. The main ingredient for the construction of X2′(p) is the generalized Dedekind eta functions.
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