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SUMMARY:Anthony Kling (U. Arizona)
DTSTART:20220421T210000Z
DTEND:20220421T220000Z
DTSTAMP:20260423T005847Z
UID:UCSD_NTS/66
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSD_NTS/66/
 ">Comparison of Integral Structures on the Space of Modular Forms of Full 
 Level $N$</a>\nby Anthony Kling (U. Arizona) as part of UCSD number theory
  seminar\n\nLecture held in APM 6402 and online.\n\nAbstract\nLet $N\\geq3
 $ and $r\\geq1$ be integers and $p\\geq2$ be a prime such that $p\\nmid N$
 . One can consider two different integral structures on the space of modul
 ar forms over $\\mathbb{Q}$\, one coming from arithmetic via $q$-expansion
 s\, 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 th
 e annihilator of the quotient. We will apply results due to Brian Conrad t
 o the situation of modular forms of even weight and level $\\Gamma(Np^{r})
 $ over $\\mathbb{Q}_{p}(\\zeta_{Np^{r}})$ to obtain an upper bound for the
  exponent. We also use Klein forms to construct explicit modular forms of 
 level $p^{r}$ whenever $p^{r}>3$\, allowing us to compute a lower bound wh
 ich agrees with the upper bound. Hence we are able to compute the exponent
  precisely.\n\npre-talk\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/66/
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