\relax \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}} \@writefile{toc}{\contentsline {section}{\numberline {2}Discriminants of Hecke Algebras}{1}} \newlabel{prop:separable}{{2.2}{1}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}The Discriminant Valuation}{2}} \@writefile{toc}{\contentsline {section}{\numberline {3}Motivation and Applications}{2}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Literature}{3}} \@writefile{toc}{\contentsline {section}{\numberline {4}Data About Discriminant Valuations}{3}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Weight Two}{3}} \newlabel{thm:disc}{{4.1}{3}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Higher Weight Data}{5}} \@writefile{toc}{\contentsline {section}{\numberline {5}The Conjecture}{5}} \newlabel{conj:big}{{5.1}{5}} \@writefile{toc}{\contentsline {section}{\numberline {6}Conjectures}{6}}