Determination of certain mod $p$ Galois representations using local constancy

Abhik Ganguli, Suneel Kumar

Let $p\ge 5$ be a prime. Let $k=b+c(p-1)$ be an integer in $[2p+2,p^2-p+3]$, where $b\in [2,p]$ and $c\in [2,p-1]$. We prove local constancy in the weight space of the…