An explicit type number formula for quaternion orders of level $(N_1,N_2)$

We give an explicit type number formula for the quaternion orders of level $(N_1,N_2)$ specified in this paper, where $N_1=p_1^{2u_1+1}\cdots p_w^{2u_w+1}$, the primes $p_i$ are distinct, $u_i\ge0$, $w$ is odd, and $\gcd(N_1,N_2)=1$. The formula includes Eichler orders and the orders with odd prime-