Non-Ordinary Primes: A Story

  title={Non-Ordinary Primes: A Story},
  author={Fernando Q. Gouv{\^e}a},
  journal={Experimental Mathematics},
This research was supported in part by grant DMS from the National Science Foundation A normalized modular eigenform f is said to be ordinary at a prime p if p does not divide the p-th Fourier coefficient of f. We take f to be a modular form of level 1 and weight k f12, 16, 18, 20, 22, 26g and search for primes where f is not ordinary. To do this, we need an efficient way to compute the reduction modulo p of the p-th Fourier coefficient. A convenient formula was known for k = 12; trying to… CONTINUE READING