Completeness of Hilbert modular surface data (awaiting review)

The database contains the Hilbert modular surfaces $X_0(\mathfrak{N})_\mathfrak{b}$ and $X_0^1(\mathfrak{N})_\mathfrak{b}$ for the

• real quadratic fields with discriminant $d \leq 3000$,
• levels $\mathfrak{N}$ bounded by $\text{Nm}(\mathfrak{N}) \leq 5000/d^{3/2}$,
• and all representatives $\mathfrak{b}$ for the narrow class group.

For each Hilbert modular surface, we compute the cusps, elliptic points, topological Euler number, holomorphic Euler characteristic, Hodge diamond, self-intersection $K^2$, and Kodaira dimension.

We have yet to compute the Kodaira dimension for 184 surfaces of type $X_0(\mathfrak{N})_\mathfrak{b}$ and 175 surfaces of type $X_0^1(\mathfrak{N})_\mathfrak{b}$. In these cases, we store a list of possibilities for the Kodaira dimension. Otherwise, the data is complete.