  The nonorientable 4-genus is an invariant of knots which has been studied by
many authors, including Gilmer and Livingston, Batson, and Ozsv\'{a}th,
Stipsicz, and Szab\'{o}. Given a nonorientable surface $F \subset B^4$ with
$\partial F = K\subset S^3$ a knot, an analysis of the existing methods for
bounding and computing the nonorientable 4-genus reveals relationships between
the first Betti number $\beta_1$ of $F$ and the normal Euler class $e$ of $F$.
This relationship yields a geography problem: given a knot $K$, what is the set
of realizable pairs $(e(F), \beta_1(F))$ where $F\subset B^4$ is a
nonorientable surface bounded by $K$? We explore this problem for families of
torus knots. In addition, we use the Ozsv\'ath-Szab\'o $d$-invariant of
two-fold branched covers to give finer information on the geography problem. We
present an infinite family of knots where this information provides an
improvement upon the bound given by Ozsv\'ath, Stipsicz, and Szab\'o using the
Upsilon invariant.
