Related papers: Computing weight one modular forms over $\C$ and $…

We compute tables of paramodular forms of degree two and cohomological weight via a correspondence with orthogonal modular forms on quinary lattices.

Let f be a newform of weight at least 3 with Fourier coefficients in a number field K. We show that the universal deformation ring of the mod lambda Galois representation associated to f is unobstructed, and thus isomorphic to a power…

Let $\Gamma_{F,n}$ be the Hermitian modular group of degree $n>1$ in sense of Hel Braun with respect to an imaginary quadratic field $F$. Let $r$ be a natural number. There exists a multiplier system of weight $1/r$ (equivalently a…

We consider mod p Hilbert modular forms associated to a totally real field of degree d in which p is unramified. We prove that every such form arises by multiplication by partial Hasse invariants from one whose weight (a d-tuple of…

We show that there are primitive holomorphic modular forms f of weight two and arbitrary large level N such that $|f(z)| \gg N^{1/4}$ for some point z. Thereby we disprove a folklore conjecture that the sup-norm of such forms would be as…

We examine canonical bases for weakly holomorphic modular forms of weight $0$ and level $p = 2, 3, 5, 7, 13$ with poles only at the cusp at $\infty$. We show that many of the Fourier coefficients for elements of these canonical bases are…

We show that certain paramodular cuspidal automorphic irreducible representations of $\mathrm{GSp}(4,\mathbb{A}_\mathbb{Q})$, which are not CAP, are globally generic. This implies a multiplicity one theorem for paramodular cuspidal…

We develop an effective algorithm to compute the derivative of a Bianchi modular form with respect to weight space as it varies in a $p$-adic family. This method is entirely local at the modular form, and does not compute the family…

In the literature, the standard approach to finding bases of spaces of modular forms is via modular symbols and the homology of modular curves. By using the Eichler-Shimura isomorphism, a work by Wang shows how one can use a cohomological…

We study the possible weights of an irreducible two-dimensional mod p representation of the absolute Galois group of F which is modular in the sense of that it comes from an automorphic form on a definite quaternion algebra with centre F…

Explicit bases for the spaces of holomorphic cusp forms of all even positive weights and all orders are constructed. The dimensions of these spaces are computed.

We study the weight part of (a generalisation of) Serre's conjecture for mod l Galois representations associated to automorphic representations on rank two unitary groups for odd primes l. We propose a conjectural set of Serre weights,…

Let $F$ be a totally real field. We prove the existence of all symmetric power liftings of those cuspidal automorphic representations of $\mathrm{GL}_2(\mathbf{A}_F)$ associated to Hilbert modular forms of regular weight.

We prove modularity of certain residually reducible ordinary 2-dimensional $p$-adic Galois representations with determinant a finite order odd character $\chi$. For certain non-quadratic $\chi$ we prove an $R=T$ result for $T$ the weight 1…

Irreducible nonzero level modules with finite-dimensional weight spaces are studied for non-twisted affine Lie superalgebras. A complete classification is obtained for superalgebras A(m,n)^ and C(n)^. In other cases the classification…

Let U^>=0 denote the half quantum group for a fixed simple Lie algebra. We examine some properties and representation of U^>=0. We prove that the Hopf algebra U^>=0 is not quasi-cocommutative, and hence the category of left U^>=0-module is…

We consider the problem of explicitly computing dimensions of spaces of automorphic or modular forms in level one, for a split classical group $\mathbf{G}$ over $\mathbb{Q}$ such that $\mathbf{G}(\R)$ has discrete series. Our main…

Recently, Bruinier and Ono classified cusp forms $f(z) := \sum_{n=0}^{\infty} a_f(n)q ^n \in S_{\lambda+1/2}(\Gamma_0(N),\chi)\cap \mathbb{Z}[[q]]$ that does not satisfy a certain distribution property for modulo odd primes $p$. In this…

We investigate the analogue of the Quantum Unique Ergodicity (QUE) conjecture for half-integral weight automorphic forms. Assuming the Generalized Riemann Hypothesis (GRH) we establish QUE for both half-integral weight holomorphic Hecke…

In this article we consider mod p modular Galois representations which are unramified at p such that the Frobenius element at p acts through a scalar matrix. The principal result states that the multiplicity of any such representation is…