Siegel Modular Forms

This page will provide a listing of degree two Siegel modular forms that appeared in my work. These Siegel modular forms might be constructed in several ways.

  1. An additive lift of a weak Jacobi form
  2. A product formula implied by Mathieu/Umbral moonshine
  3. A product of scaled Borcherds products

Siegel modular forms for Mathieu Moonshine

Let $\rho=[g]$ be a conjugacy class of and element $g$ of $M_{24}$, the largest sporadic simple group discovered by Mathieu. To each of the 26 conjugacy classes we will describe the Siegel modular form in 2-3 ways as described above. The additive lift is not available for all conjugacy classes.

Conj Class Weight Level Character Modular Form Data
$1^{24}$ (1A) $10$ $1$ $\Phi_{10}$ 1A Data
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Siegel modular forms for Umbral Moonshine

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