We give upper bounds on the size of the gap between the constant term
and the next nonzero Fourier coefficient of an entire modular form of
given weight for $\flop{L}{-.3}\!_0(2)$. Numerical evidence indicates that a
sharper bound holds for the weights $h \equiv 2 \pmod 4$. We derive
upper bounds for the minimum positive integer represented by level-two
even positive-definite quadratic forms. Our data suggest that, for
certain meromorphic modular forms and $p=2$, $3$, the $p$-order of the
constant term is related to the base-$p$ expansion of the order of the
pole at infinity.