5 problems

Atkin–Swinnerton-Dyer conjecture. One has $N=1$ if and only if the subgroup contains a congruence subgroup. This conjecture concerns the integrality of Fourier coefficients for mod…

Let $\Gamma$ be a noncongruence subgroup of $SL_2(\mathbb Z)$ with finite index, let $k\geq 2$, and let $S_k(\Gamma)$ have dimension $d$. Denote by $X_{\Gamma}$ the modular curve a…

Unbounded denominators conjecture. Every noncongruence group satisfies condition (UBD).

Let $h_1,h_2$ be the indicated basis of $S_3(\Gamma_{8^3.6.3.1^3})$, let $f$ be the congruence form given earlier in the source, and let $\chi$ be a certain Hecke character. For pr…

Let $f$ denote the congruence form whose coefficients are compared with the Atkin–Swinnerton-Dyer data for the forms $h_1,h_2$ on $\Gamma_{8^3.2^3.3^3}$. An associated congruence-f…