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Invariants of Modular Abelian
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Level Raising and Lowering
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Level Raising and Lowering
Contents
Problems
Let
be a newform in
(or, more generally, in
). Let
be a prime ideal in the ring generated by the Fourier coefficients of
. Let
be a positive integer.
Problem 7.1.1
Let
be the elliptic curve 11a given by the equation
and let
be the corresponding newform. For
compute all newforms
with
prime and
. Is there a pattern?
Problem 7.1.2
Formulate a level raising conjecture modulo
. Provide computational and theoretical evidence.
Problem 7.1.3
Formulate a level lowering conjecture modulo
. Provide computational and theoretical evidence.
William Stein 2006-10-20