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Principal Congruence Subgroups of the Hecke Groups

✍ Scribed by Mong-Lung Lang; Chong-Hai Lim; Ser-Peow Tan

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 126 KB
Volume: 85
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2000.2542

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✦ Synopsis

Let q be an odd integer >3 and let G q be the Hecke group associated to q. Let ({) be a prime ideal of Z[* q ] and G(q, {) the principal congruence subgroup of G q associated to {. We give a formula for [G q : G(q, {)], the index of the principal congruence subgroup G(q, {) in G q . We also give formulae for the indices [G 1 (q, {), G(q, {)] and [G 0 (q, {), G 1 (q, {)]. Finally, we give a formula for the geometric invariants of G(q, {) when q is a rational prime.

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