Search

For a modular elliptic curve $E/\mathbb{Q}$, we show a number of links between the primes $\ell $ for which the mod $\ell $ representation of $E/\mathbb{Q}$ has projective dihedral image and congruence primes for the newform associated to $E/\mathbb{Q}$.

Let f be a primitive Hilbert modular cusp form of arbitrary level and parallel weight k, defined over a totally real number field F. We define a finite set of primes $\cal S$ that depends on the weight and level of f, the field F, and the torsion in the boundary cohomology groups of the Borel–Serre compactification of the underlying Hilbert-Blumenthal variety. We show that, outside $\cal S$, any prime that divides the algebraic part of the value at s=1 of the adjoint L-function of f is a congruence prime for f. In special cases we identify the ‘boundary primes’ in terms of expressions of the form $N_{F/{\mathbb{Q}}}(\epsilon^{k-1} - 1)$, where ε is a totally positive unit of F.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

Surjectivity of mod ℓ Representations Attached to Elliptic Curves and Congruence Primes

Adjoint L-Values and Primes of Congruence for Hilbert Modular Forms

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

Surjectivity of mod ℓ Representations Attached to Elliptic Curves and Congruence Primes

Adjoint L-Values and Primes of Congruence for Hilbert Modular Forms