Congruences for modular forms of weights two and four

AbstractWe prove a conjecture of Calegari and Stein regarding mod p congruences between modular forms of weight four and the derivatives of modular forms of weight two

Conjectures about discriminants of Hecke algebras at prime level

We study p-divisibility of discriminants of Hecke algebras associated to spaces of cusp forms of prime level. We make a precise conjecture about the indexes of Hecke algebras in their normalisation which implies (if true) the conjecture that there are no mod p congruences between non-conjugate newforms of weight 2 and level Gamma_0(p).Comment: To appear in ANTS 6 Proceeding

On mod p\mathfrak{p} congruences for Drinfeld modular forms of level pm\mathfrak{p}\mathfrak{m}

In~\cite{CS04}, Calegari and Stein studied the congruences between classical cusp forms $S_k(\Gamma_0(p))$ of prime level and made several conjectures about them. In~\cite{AB07} (resp., ~\cite{BP11}) the authors proved one of those conjectures (resp., their generalizations). In this article, we study the analogous conjecture and its generalizations for Drinfeld modular forms