The density of primes for which the first coefficient of U_l(eta^r) is odd is proven to exist, is classified, bounded, and computed for dihedral CM families.
Bellaïche, Formes spéciales modulaires modulo 2 , to appear in Tunisian Journal of Mathematics
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On the parity of coefficients of eta powers
The density of primes for which the first coefficient of U_l(eta^r) is odd is proven to exist, is classified, bounded, and computed for dihedral CM families.