1. CJM 2017 (vol 70 pp. 241)
 Böcherer, Siegfried; Kikuta, Toshiyuki; Takemori, Sho

Weights of the mod $p$ kernel of the theta operators
Let $\Theta ^{[j]}$ be an analogue of the Ramanujan theta operator
for Siegel modular forms.
For a given prime $p$, we give the weights of elements of mod
$p$ kernel of $\Theta ^{[j]}$,
where the mod $p$ kernel of $\Theta ^{[j]}$ is the set of all
Siegel modular forms $F$ such that $\Theta ^{[j]}(F)$ is congruent
to zero modulo $p$.
In order to construct examples of the mod $p$ kernel of $\Theta
^{[j]}$ from any Siegel modular form,
we introduce new operators $A^{(j)}(M)$ and show the modularity
of $FA^{(j)}(M)$ when $F$ is a Siegel modular form.
Finally, we give some examples of the mod $p$ kernel of $\Theta
^{[j]}$ and the filtrations of some of them.
Keywords:Siegel modular form, congruences for modular forms, Fourier coefficients, Ramanujan's operator, filtration Categories:11F33, 11F46 

2. CJM 2017 (vol 70 pp. 1076)
 Martin, Kimball

Congruences for Modular Forms mod 2 and Quaternionic $S$ideal Classes
We prove many simultaneous congruences mod 2 for elliptic and
Hilbert modular forms
among forms with different AtkinLehner eigenvalues. The proofs
involve the notion of quaternionic $S$ideal classes and the
distribution of AtkinLehner signs among
newforms.
Keywords:modular forms, congruences, quaternion algebras Categories:11F33, 11R52 

3. CJM 2016 (vol 68 pp. 961)
4. CJM 2016 (vol 68 pp. 1227)
 Brasca, Riccardo

Eigenvarieties for Cuspforms over PEL Type Shimura Varieties with Dense Ordinary locus
Let $p \gt 2$ be a prime and let $X$ be a compactified PEL Shimura
variety of type (A) or (C) such that $p$ is an unramified prime
for the PEL datum and such that the ordinary locus is dense in
the reduction of $X$. Using the geometric approach of Andreatta,
Iovita, Pilloni, and Stevens we define the notion of families
of overconvergent locally analytic $p$adic modular forms of
Iwahoric level for $X$. We show that the system of eigenvalues
of any finite slope cuspidal eigenform of Iwahoric level can
be deformed to a family of systems of eigenvalues living over
an open subset of the weight space. To prove these results, we
actually construct eigenvarieties of the expected dimension that
parameterize finite slope systems of eigenvalues appearing in
the space of families of cuspidal forms.
Keywords:$p$adic modular forms, eigenvarieties, PELtype Shimura varieties Categories:11F55, 11F33 

5. CJM 2012 (vol 66 pp. 170)
 Guitart, Xavier; Quer, Jordi

Modular Abelian Varieties Over Number Fields
The main result of this paper is a characterization of the abelian
varieties $B/K$ defined over Galois number fields with the
property that the $L$function $L(B/K;s)$ is a product of
$L$functions of nonCM newforms over $\mathbb Q$ for congruence
subgroups of the form $\Gamma_1(N)$. The characterization involves the
structure of $\operatorname{End}(B)$, isogenies between the Galois conjugates of
$B$, and a Galois cohomology class attached to $B/K$.
We call the varieties having this property strongly modular.
The last section is devoted to the study of a family of abelian surfaces with quaternionic
multiplication.
As an illustration of the ways in which the general results of the paper can be applied
we prove the strong modularity of some particular abelian surfaces belonging to that family, and
we show how to find nontrivial examples of strongly modular varieties by twisting.
Keywords:Modular abelian varieties, $GL_2$type varieties, modular forms Categories:11G10, 11G18, 11F11 

6. CJM 2012 (vol 65 pp. 403)
 Van Order, Jeanine

On the Dihedral Main Conjectures of Iwasawa Theory for Hilbert Modular Eigenforms
We construct a bipartite Euler system in the sense of Howard for Hilbert modular eigenforms of parallel
weight two over totally real fields, generalizing works of BertoliniDarmon, Longo, Nekovar, PollackWeston
and others. The construction has direct applications to Iwasawa main conjectures. For instance, it implies
in many cases one divisibility of the associated dihedral or anticyclotomic main conjecture, at the same
time reducing the other divisibility to a certain nonvanishing criterion for the associated $p$adic $L$functions.
It also has applications to cyclotomic main conjectures for Hilbert modular forms over CM fields via the technique
of Skinner and Urban.
Keywords:Iwasawa theory, Hilbert modular forms, abelian varieties Categories:11G10, 11G18, 11G40 

7. CJM 2011 (vol 64 pp. 588)
8. CJM 2011 (vol 64 pp. 282)