Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 Atkin--Lehner eigenvalues. The proofs involve
the notion of quaternionic $S$-ideal classes and the distribution of
Atkin--Lehner signs among newforms.

19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph