Estimation of Genus for Certain Arithmetic Groups

Abstract

We find the genera of arithmetic groups ⟨Γ₁(N), Φ⟩ for N ≥ 1 and Φ the Fricke involution, from which we derive that the genus g(⟨Γ₁(N), Φ⟩) is zero if and only if 1 ≤ N ≤ 12 and N = 14, 15.

Key Words:

• Arithmetic group
• Modular curve
• Class number

AMS Classification:

• 11G30
• 14H55

Acknowledgment

Supported by KOSEF Research Grant 98-0701-01-01-3.

Notes

^#Communicated by D. Easdown.