Abstract
We develop geometric methods to study the generating weights of free modules of vector-valued modular forms of half-integral weight, taking values in a complex representation of the metaplectic group. We then compute the generating weights for modular forms taking values in the Weil representation attached to cyclic quadratic modules of order $2p^r$, where $p \geq 5$ is a prime. We also show that the generating weights approach a simple limiting distribution as $p$ grows, or as $r$ grows and $p$ remains fixed.
| Original language | English |
|---|---|
| Pages (from-to) | 474-497 |
| Number of pages | 24 |
| Journal | Journal of Number Theory |
| Volume | 180 |
| Early online date | 23 Jun 2017 |
| DOIs | |
| Publication status | Published - 1 Nov 2017 |
Keywords
- vector-valued modular form
- half-integral weight
- Weil representation
- quadratic module
- generating weights
- metaplectic group
- metaplectic orbifold
- critical weights
- Serre duality
- Dirichlet class number formula
- imaginary quadratic field
- positive-definite lattice
- quadratic form
- theta function