Jaclyn Lang

activity

20092026

most citedOn the image of the Galois representation associated to a non-CM Hida family

9 citations · 9 across the 9 of their papers we have counts for

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Showing 2026 · math.NTShow all

3 papers · 2 filters

math.NT2026

Counting level-raising congruences using modular representation theory

Jaclyn Lang, Robert Pollack, Preston Wake

We introduce a new method for studying mod- $ℓ$ congruences between eigenforms through the modular representation theory of $PGL_{2} (F_{p})$ . When $p\equiv \pm 1 \p…

math.NT2026

Modularity theorems for Eisenstein congruences in prime-power level

Jaclyn Lang, Katharina Müller, Bharathwaj Palvannan

Let $p, N \geq 5$ be primes such that $N \equiv 1 mod p$ . We prove modularity theorems at levels $N$ and $N^{2}$ , showing that suitable Eisenstein localizations of the weight- $2$ $…

math.NT2026

A new perspective on the rank of Mazur's Eisenstein Hecke algebra

Jaclyn Lang, Katharina Müller, Bharathwaj Palvannan

Let $N, p \geq 5$ be primes such that $N \equiv 1 mod p$ . We study the rank $r$ of the Hecke algebra that parametrizes modular forms of weight 2 and level $N$ that are Eisenstein…