8 citations · 17 across the 6 of their papers we have counts for
9 papers
Prime-power congruences for level-one eigenforms
Nadim Rustom
We study prime-power congruences for the prime-to-\(p\) Hecke eigensystems of normalized cuspidal level-one eigenforms as the weight varies, and we address the problem of classifyi…
Eisenstein series, -adic modular functions, and overconvergence, II
Ian Kiming, Nadim Rustom
Let be a prime number. Continuing and extending our previous paper with the same title, we prove explicit rates of overconvergence for modular functions of the form $\frac{E_k^…
Eisenstein series, p-adic modular functions, and overconvergence
Ian Kiming, Nadim Rustom
Let be a prime . We establish explicit rates of overconvergence for members of the "Eisenstein family", notably for the -adic modular function $V(E_{(1,0)}^{\ast})/E_…
Dihedral Group, 4-Torsion on an Elliptic Curve, and a Peculiar Eigenform Modulo 4
Ian Kiming, Nadim Rustom
We work out a non-trivial example of lifting a so-called weak eigenform to a true, characteristic 0 eigenform. The weak eigenform is closely related to Ramanujan's tau function whe…
Congruences modulo prime powers of Hecke eigenvalues in level
Nadim Rustom
We continue the study of strong, weak, and -weak eigenforms introduced by Chen, Kiming, and Wiese. We completely determine all systems of Hecke eigenvalues of level modulo…
Filtrations of dc-weak eigenforms
Nadim Rustom
The notions of strong, weak and dc-weak eigenforms mod was introduced and studied by Chen, Kiming and Wiese. In this work, we prove that there can be no uniform weight bound…
On certain finiteness questions in the arithmetic of modular forms
Ian Kiming, Nadim Rustom, Gabor Wiese
We investigate certain finiteness questions that arise naturally when studying approximations modulo prime powers of p-adic Galois representations coming from modular forms. We lin…
Generators and relations of the graded algebra of modular forms
Nadim Rustom
We give bounds on the degree of generators for the ideal of relations of the graded algebras of modular forms with coefficients in over congruence subgroups f…
Generators of graded rings of modular forms
Nadim Rustom
We study graded rings of modular forms over congruence subgroups, with coefficients in a subring of , and specifically the highest weight needed to generate these r…