Large values of modular forms
  We show that there are primitive holomorphic modular forms f of weight two and arbitrary large level N such that $|f(z)| \gg N^{1/4}$ for some point z. Thereby we disprove a folklore conjecture that the sup-norm of such forms would be as small as $N^{o(1)}$. 
Nicolas Templier
math.NT math.RT