On Modular Forms for the Paramodular Groups

Theta lifts of Bianchi modular forms and applications to paramodularity

“…For the paramodular group Γ p (N ), the theory of newforms developed in [30,31] for scalar weights carries over to the vector-valued setting. The old subspace is generated by the images of the level-raising maps of [30].…”

“…For the paramodular group Γ p (N ), the theory of newforms developed in [30,31] for scalar weights carries over to the vector-valued setting. The old subspace is generated by the images of the level-raising maps of [30]. One then defines the new subspace S new (k,2) (Γ p (N )) to be its orthogonal complement with respect to the Petersson inner product for vector-valued forms given in [1].…”

Survey Article: Characterizations of the Saito-Kurokawa lifting

“…In [21], it is proved, under the assumption of the Ramanujan Conjecture, that a Siegel modular form lies in the Maass space if and only if there exists a prime p such that F lies in the Maass p-space. This is an improvement of the previously described result.…”

Siegel modular forms of genus $2$ attached to elliptic curves

“…So, in particular, if p divides M exactly once, then by appealing to [41], we see that Π p must in fact contain a non-zero vector v which is invariant under the Iwahori congruence subgroup K p,I (M ) defined in the statement of Theorem C, part (a), in the Introduction, and it is not unramified for a maximal compact subgroup. Again, it is helpful to note that for non-square-free N , there is no good candidate for the "conductor", and the space of vectors fixed by K(M ) need not be 1-dimensional; for an approach in the paramodular setting, see [39].…”