{"id":{"repo_id":"arizona-thes","oai_identifier":"oai:repository.arizona.edu:10150/661567"},"canonical_url":"https://search.dev.ndltd.org/etd/arizona-thes/oai:repository.arizona.edu:10150/661567","repository":{"repo_id":"arizona-thes","name":"University of Arizona","base_url":"https://repository.arizona.edu/oai/request"},"display":{"title":"Comparison of Integral Structures on the Space of Modular Forms of Full Level N","abstract":"Let N≥3 and r≥1 be integers and p≥2 be a prime such that p∤N. One can consider two different integral structures on the space of modular forms over the rationals Q, one coming from arithmetic via q-expansions, the other coming from geometry via integral models of modular curves. Both structures are stable under the Hecke operators; furthermore, their quotient is finite torsion. Our goal is to investigate the exponent of the annihilator of the quotient. We will apply tools from Conrad to the situation of weight 2 and level Γ(Np^r) modular forms over Qp adjoin a Np^r root of unity to obtain an upper bound for the exponent. We also use Klein forms to construct explicit modular forms of level p, allowing us to compute a lower bound. When r=1, both bounds agree, allowing us to compute the exponent precisely in this case.","abstract_html":"Let N≥3 and r≥1 be integers and p≥2 be a prime such that p∤N. One can consider two different integral structures on the space of modular forms over the rationals Q, one coming from arithmetic via q-expansions, the other coming from geometry via integral models of modular curves. Both structures are stable under the Hecke operators; furthermore, their quotient is finite torsion. Our goal is to investigate the exponent of the annihilator of the quotient. We will apply tools from Conrad to the situation of weight 2 and level Γ(Np^r) modular forms over Qp adjoin a Np^r root of unity to obtain an upper bound for the exponent. We also use Klein forms to construct explicit modular forms of level p, allowing us to compute a lower bound. When r=1, both bounds agree, allowing us to compute the exponent precisely in this case.","abstract_has_math":false,"creators":["Kling, Anthony"],"institution":"The University of Arizona.","degree_name":"Ph.D.","degree_level":"doctoral","degree_discipline":"Graduate College","degree_department":null,"school":null,"contributors":[],"advisors":["Cais, Bryden R."],"committee_chairs":[],"committee_members":["Levin, Brandon","Ulmer, Douglas","Xue, Hang"],"year":2021,"date_issued":"2021","date_published":"2021","updated_at":"2026-07-24T00:57:57Z","subjects":["full level","integral structures","modular forms"],"languages":["en"],"rights":["Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction, presentation (such as public display or performance) of protected items is prohibited except with permission of the author."],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10150/661567","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Cais, Bryden R."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Levin, Brandon","Ulmer, Douglas","Xue, Hang"]},{"key":"dc:creator","label":"Author","values":["Kling, Anthony"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2021-09-10T19:05:30Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2021-09-10T19:05:30Z"]},{"key":"dc:date.issued","label":"Date","values":["2021"]},{"key":"dc:publisher","label":"Institution","values":["The University of Arizona."]},{"key":"dc:type","label":"Dc Type","values":["text","Electronic Dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Graduate College","Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Arizona"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["full level","integral structures","modular forms"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction, presentation (such as public display or performance) of protected items is prohibited except with permission of the author."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10150/661567"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Let N≥3 and r≥1 be integers and p≥2 be a prime such that p∤N. One can consider two different integral structures on the space of modular forms over the rationals Q, one coming from arithmetic via q-expansions, the other coming from geometry via integral models of modular curves. Both structures are stable under the Hecke operators; furthermore, their quotient is finite torsion. Our goal is to investigate the exponent of the annihilator of the quotient. We will apply tools from Conrad to the situation of weight 2 and level Γ(Np^r) modular forms over Qp adjoin a Np^r root of unity to obtain an upper bound for the exponent. We also use Klein forms to construct explicit modular forms of level p, allowing us to compute a lower bound. When r=1, both bounds agree, allowing us to compute the exponent precisely in this case."]},{"key":"dc:title","label":"Title","values":["Comparison of Integral Structures on the Space of Modular Forms of Full Level N"]}]}],"canonical_facts":{"dc:contributor.advisor":["Cais, Bryden R."],"dc:contributor.committeemember":["Levin, Brandon","Ulmer, Douglas","Xue, Hang"],"dc:creator":["Kling, Anthony"],"dc:date.accessioned":["2021-09-10T19:05:30Z"],"dc:date.available":["2021-09-10T19:05:30Z"],"dc:date.issued":["2021"],"dc:description.abstract":["Let N≥3 and r≥1 be integers and p≥2 be a prime such that p∤N. One can consider two different integral structures on the space of modular forms over the rationals Q, one coming from arithmetic via q-expansions, the other coming from geometry via integral models of modular curves. Both structures are stable under the Hecke operators; furthermore, their quotient is finite torsion. Our goal is to investigate the exponent of the annihilator of the quotient. We will apply tools from Conrad to the situation of weight 2 and level Γ(Np^r) modular forms over Qp adjoin a Np^r root of unity to obtain an upper bound for the exponent. We also use Klein forms to construct explicit modular forms of level p, allowing us to compute a lower bound. When r=1, both bounds agree, allowing us to compute the exponent precisely in this case."],"dc:identifier.uri":["http://hdl.handle.net/10150/661567"],"dc:language.iso":["en"],"dc:publisher":["The University of Arizona."],"dc:rights":["Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction, presentation (such as public display or performance) of protected items is prohibited except with permission of the author."],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["full level","integral structures","modular forms"],"dc:title":["Comparison of Integral Structures on the Space of Modular Forms of Full Level N"],"dc:type":["text","Electronic Dissertation"],"thesis:degree_discipline":["Graduate College","Mathematics"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Arizona"]},"updated_at":"2026-07-24T00:57:57Z"}