{"id":38,"date":"2018-01-08T16:32:25","date_gmt":"2018-01-08T16:32:25","guid":{"rendered":"https:\/\/math-sites.uncg.edu\/number-theory\/?p=38"},"modified":"2025-01-24T19:37:57","modified_gmt":"2025-01-24T19:37:57","slug":"congruence","status":"publish","type":"post","link":"https:\/\/math-sites.uncg.edu\/number-theory\/congruence\/","title":{"rendered":"Congruence Subgroups of $$\\textrm{PSL}(2,\\mathbb{Z})$$"},"content":{"rendered":"
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
^<\/a><\/th>\nLevel\u00a019<\/th>\nName<\/td>\nIndex<\/td>\n\u00a0con<\/td>\n\u00a0len<\/td>\n\u00a0c2<\/sub><\/td>\n\u00a0c3<\/sub><\/td>\n><\/a><\/th>\nCusps<\/td>\nGal<\/td>\n\u00a0Supergroups<\/td>\n\u00a0Subgroups<\/td>\n<\/tr>\n
<\/td>\n19A14<\/sup><\/th>\n<\/td>\n285<\/td>\n1<\/td>\n285<\/td>\n5<\/td>\n6<\/td>\n<\/td>\n1915<\/sup><\/td>\n61\u00a0\u00a0<\/sup>91\u00a0\u00a0<\/sup>1815<\/sup><\/td>\n19A2<\/sup><\/a><\/td>\n<\/tr>\n
^<\/a><\/th>\nLevel\u00a021<\/th>\nName<\/td>\nIndex<\/td>\n\u00a0con<\/td>\n\u00a0len<\/td>\n\u00a0c2<\/sub><\/td>\n\u00a0c3<\/sub><\/td>\n><\/a><\/th>\nCusps<\/td>\nGal<\/td>\n\u00a0Supergroups<\/td>\n\u00a0Subgroups<\/td>\n<\/tr>\n
<\/td>\n21A14<\/sup><\/th>\n<\/td>\n252<\/td>\n2<\/td>\n63<\/td>\n8<\/td>\n0<\/td>\n<\/td>\n2112<\/sup><\/td>\n67\u00a0\u00a0<\/sup>127<\/sup><\/td>\n21B4<\/sup><\/a> 21D5<\/sup><\/a> 21C6<\/sup><\/a><\/td>\n<\/tr>\n
^<\/a><\/th>\nLevel\u00a025<\/th>\nName<\/td>\nIndex<\/td>\n\u00a0con<\/td>\n\u00a0len<\/td>\n\u00a0c2<\/sub><\/td>\n\u00a0c3<\/sub><\/td>\n><\/a><\/th>\nCusps<\/td>\nGal<\/td>\n\u00a0Supergroups<\/td>\n\u00a0Subgroups<\/td>\n<\/tr>\n
<\/td>\n25A14<\/sup><\/th>\n<\/td>\n250<\/td>\n1<\/td>\n250<\/td>\n10<\/td>\n1<\/td>\n<\/td>\n2510<\/sup><\/td>\n101\u00a0\u00a0<\/sup>2012<\/sup><\/td>\n5C0<\/sup><\/a><\/td>\n<\/tr>\n
^<\/a><\/th>\nLevel\u00a028<\/th>\nName<\/td>\nIndex<\/td>\n\u00a0con<\/td>\n\u00a0len<\/td>\n\u00a0c2<\/sub><\/td>\n\u00a0c3<\/sub><\/td>\n><\/a><\/th>\nCusps<\/td>\nGal<\/td>\n\u00a0Supergroups<\/td>\n\u00a0Subgroups<\/td>\n<\/tr>\n
<\/td>\n28A14<\/sup><\/th>\n<\/td>\n252<\/td>\n2<\/td>\n63<\/td>\n8<\/td>\n0<\/td>\n<\/td>\n146<\/sup>
\n286<\/sup><\/td>\n		621<\/sup><\/td>\n14G5<\/sup><\/a> 28J6<\/sup><\/a> 28C7<\/sup><\/a><\/td>\n<\/tr>\n
<\/td>\n28B14<\/sup><\/th>\n<\/td>\n252<\/td>\n2<\/td>\n63<\/td>\n8<\/td>\n0<\/td>\n<\/td>\n146<\/sup>
\n286<\/sup><\/td>\n		621<\/sup><\/td>\n28H5<\/sup><\/a> 14A6<\/sup><\/a> 28C7<\/sup><\/a><\/td>\n<\/tr>\n
<\/td>\n28C14<\/sup><\/th>\n<\/td>\n252<\/td>\n2<\/td>\n63<\/td>\n8<\/td>\n0<\/td>\n<\/td>\n146<\/sup>
\n286<\/sup><\/td>\n		621<\/sup><\/td>\n28C4<\/sup><\/a> 14A6<\/sup><\/a> 28I6<\/sup><\/a> 28J6<\/sup><\/a><\/td>\n<\/tr>\n
^<\/a><\/th>\nLevel\u00a030<\/th>\nName<\/td>\nIndex<\/td>\n\u00a0con<\/td>\n\u00a0len<\/td>\n\u00a0c2<\/sub><\/td>\n\u00a0c3<\/sub><\/td>\n><\/a><\/th>\nCusps<\/td>\nGal<\/td>\n\u00a0Supergroups<\/td>\n\u00a0Subgroups<\/td>\n<\/tr>\n
<\/td>\n30A14<\/sup><\/th>\n<\/td>\n240<\/td>\n1<\/td>\n240<\/td>\n0<\/td>\n3<\/td>\n<\/td>\n106<\/sup>
\n306<\/sup><\/td>\n		430\u00a0\u00a0<\/sup>815<\/sup><\/td>\n10J1<\/sup><\/a> 30I5<\/sup><\/a><\/td>\n<\/tr>\n
^<\/a><\/th>\nLevel\u00a031<\/th>\nName<\/td>\nIndex<\/td>\n\u00a0con<\/td>\n\u00a0len<\/td>\n\u00a0c2<\/sub><\/td>\n\u00a0c3<\/sub><\/td>\n><\/a><\/th>\nCusps<\/td>\nGal<\/td>\n\u00a0Supergroups<\/td>\n\u00a0Subgroups<\/td>\n<\/tr>\n
<\/td>\n31A14<\/sup><\/th>\n<\/td>\n248<\/td>\n2<\/td>\n248<\/td>\n8<\/td>\n5<\/td>\n<\/td>\n318<\/sup><\/td>\n61\u00a0\u00a0<\/sup>101\u00a0\u00a0<\/sup>3016<\/sup><\/td>\n1A0<\/sup><\/a><\/td>\n<\/tr>\n
^<\/a><\/th>\nLevel\u00a032<\/th>\nName<\/td>\nIndex<\/td>\n\u00a0con<\/td>\n\u00a0len<\/td>\n\u00a0c2<\/sub><\/td>\n\u00a0c3<\/sub><\/td>\n><\/a><\/th>\nCusps<\/td>\nGal<\/td>\n\u00a0Supergroups<\/td>\n\u00a0Subgroups<\/td>\n<\/tr>\n
<\/td>\n32A14<\/sup><\/th>\n<\/td>\n256<\/td>\n1<\/td>\n256<\/td>\n16<\/td>\n1<\/td>\n<\/td>\n328<\/sup><\/td>\n1616<\/sup><\/td>\n16G2<\/sup><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Part of a table of all congruence subgroups of Genus 14, which is included in a collection of tables of all congruence subgroups of PSL(2,$$\\mathbb{Z})$$ of genus up to 24<\/a>. The algorithm used to generate these tables is described in the article Congruence Subgroups of PSL(2,$$\\mathbb{Z})$$ of Genus up to 24<\/a> by Chris Cummins<\/a> and Sebastian Pauli<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

^ Level\u00a019 Name Index \u00a0con \u00a0len \u00a0c2 \u00a0c3 > Cusps Gal \u00a0Supergroups \u00a0Subgroups 19A14 285 1 285 5 6 1915 61\u00a0\u00a091\u00a0\u00a01815 19A2…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[8],"tags":[],"class_list":["post-38","post","type-post","status-publish","format-standard","hentry","category-number-theory"],"acf":[],"_links":{"self":[{"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/posts\/38","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/comments?post=38"}],"version-history":[{"count":7,"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/posts\/38\/revisions"}],"predecessor-version":[{"id":230,"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/posts\/38\/revisions\/230"}],"wp:attachment":[{"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/media?parent=38"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/categories?post=38"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math-sites.uncg.edu\/number-theory\/wp-json\/wp\/v2\/tags?post=38"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}