Comparison of Integral Structures on the Space of Modular Forms of Full Level N

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Graduate College

Grantor dc:publisher

The University of Arizona.

Year dc:date.issued

2021

Author dc:creator

• Kling, Anthony

Advisor dc:contributor.advisor

• Cais, Bryden R.

Committee members dc:contributor.committeemember

• Levin, Brandon
• Ulmer, Douglas
• Xue, Hang

• full level
• integral structures
• modular forms

Statement 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.

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10150/661567

OAI identifier oai:identifier

oai:repository.arizona.edu:10150/661567