8 problems

Let $f_i(\tau)$ be a component of a vector-valued modular form with Fourier expansion … where $n^{(i)}_0=p_i/N_i$ and $(p_i,N_i)=1$. Suppose that all coefficients $a_n^{(i)}$ are a…

Let $\rho$ be a representation and let $\widetilde{M}_n(k,\rho,\widetilde{\Gamma})$ denote the corresponding space of vector-valued Siegel modular forms. Vector-valued generalizati…

Let $\vec f(\tau)$ be a vector-valued modular form (vvmf) whose Fourier expansions have rational exponents, and suppose its Fourier coefficients are integral. Integrality conjectur…

Let $\vec v(q)$ be a vector-valued modular function with components $v_i(q)$, and write the Fourier expansion of $v_i(q)$ with leading exponent $m_0^{(i)}$ and Fourier coefficients…

Let $\rho$ be an irreducible representation, and let $m_k$ denote the multiplicity of forms of even weight $k$ among a free basis for $M(\rho)$ over the ring of scalar-valued modul…

Let $S_{j,2}(Gamma_2,epsilon)$ denote the space of Siegel cusp forms of degree $2$, weight $(j,2)$, and character $epsilon$. The character-valued vanishing conjecture states that ……

Let $S_{j,2}(Gamma_2[2])$ denote the space of vector-valued Siegel modular forms of degree $2$, weight $(j,2)$, and level $Gamma_2[2]$. A Yoshida-lift generation conjecture. The sp…

Let $\Gamma=SL_2(\mathbb{Z})$, let $\rho$ be a representation of $\Gamma$, and let $F$ be a vector-valued modular form for $\rho$. Say that the components of $F$ have Fourier expan…