## Experimental Mathematics

### Quadratic minima and modular forms

Barry Brent

#### Abstract

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.

#### Article information

Source
Experiment. Math., Volume 7, Issue 3 (1998), 257-274.

Dates
First available in Project Euclid: 14 March 2003