BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Anna Medvedovsky (Boston University) DTSTART:20211013T143000Z DTEND:20211013T153000Z DTSTAMP:20260423T024720Z UID:UCDANT/23 DESCRIPTION:Title: Counting modular forms with fixed mod-$p$ Galois representation and Atkin- Lehner-at-$p$ eigenvalue\nby Anna Medvedovsky (Boston University) as p art of Dublin Algebra and Number Theory Seminar\n\n\nAbstract\nWork in pro gress joint with Samuele Anni and Alexandru Ghitza. For $N$ prime to $p$\, we count the number of classical modular forms of level $Np$ and weight $ k$ with fixed mod-$p$ Galois representation and Atkin-Lehner-at-$p$ sign\, generalizing both recent results of Martin generalizing work of Wakatsuki and Yamauchi (no residual representation constraint) and the $\\overline{ \\rho}$-dimension-counting formulas of Bergdall-Pollack and Jochnowitz. Wo rking with the Atkin-Lehner involution typically requires inverting $p$\, which naturally complicates investigations modulo $p$. To resolve this ten sion\, we use the trace formula to establish up-to-semisimplifcation isomo rphisms between certain mod-$p$ Hecke modules (namely\, refinements of the weight-filtration graded pieces $W_k$) by exhibiting ever-deeper congruen ces between traces of prime-power Hecke operators acting on characteristic -zero Hecke modules. This last technique\, relying on our refinement of a special case of Brauer-Nesbitt\, is new\, purely algebraic\, and may well be of independent interest. We will begin with this algebra theorem\, then discuss the classical Atkin-Lehner dimension split\, and only then move o n to our refined dimension-counting results.\n LOCATION:https://researchseminars.org/talk/UCDANT/23/ END:VEVENT END:VCALENDAR