• Bulletin of the Korean Mathematical Society
• /
• v.49 no.6
• /
• pp.1349-1357
• /
• 2012

We prove a congruence modulo a prime of Fourier coefficients of several meromorphic modular forms of low weights. We prove the result by establishing a generalization of a theorem of Garthwaite.

• Journal of the Chungcheong Mathematical Society
• /
• v.30 no.4
• /
• pp.445-447
• /
• 2017

We investigate congruence properties of Fourier coefficients of modular forms for ${\Gamma}^+_0(2)$.

• Journal of the Korean Mathematical Society
• /
• v.53 no.6
• /
• pp.1445-1457
• /
• 2016

For a positive integer N divisible by 4, let ${\mathcal{O}}^1_N({\mathbb{Q}})$ be the ring of weakly holomorphic modular functions for the congruence subgroup ${\Gamma}^1(N)$ with rational Fourier coefficients. We present explicit generators of the ring ${\mathcal{O}}^1_N({\mathbb{Q}})$ over ${\mathbb{Q}}$ in terms of both Fricke functions and Siegel functions, from which we are able to classify all Fricke families of such level N.

• Journal of the Korean Mathematical Society
• /
• v.61 no.5
• /
• pp.997-1033
• /
• 2024

We use Borcherds products to give a new construction of the weight 3 paramodular nonlift eigenform f_N for levels N = 61, 73, 79. We classify the congruences of f_N to Gritsenko lifts. We provide techniques that compute eigenvalues to support future modularity applications. Our method does not compute Hecke eigenvalues from Fourier coefficients but instead uses elliptic modular forms, specifically the restrictions of Gritsenko lifts and their images under the slash operator to modular curves.