Voozh

A135362

Index of the Hecke algebra in its saturation in End(J_0(n)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 4, 1, 1, 1, 2, 1, 1, 1, 8, 1, 1, 1, 16, 1, 4, 1, 8, 1, 1, 9, 1, 1, 1, 1, 4, 1

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OFFSET

1,44

COMMENTS

"A quantity that controls the relation between the modular degree and congruences (the "congruence modulus"). This results in the following table, which suggests that if p | a(n) is a prime, then p^2 | 4 * n,a fact closely related to what Ken Ribet proved at the Raynaud birthday conference in Orsay a few years ago. Also, Mazur proved that a(p) = 1 when p is prime."

LINKS

Jason Kimberley, Table of n, a(n) for n = 1..209

Yuri I. Manin, Iterated Modular Symbols.

William Stein, Modular Symbols, Modular Forms and Modular Abelian Varieties in MAGMA. See table p. 54.

PROG

(Magma) function f(N) J := JZero(N); T := HeckeAlgebra(J); return Index(Saturation(T), T); end function; for N in [1..120] do print N, f(N); end for;

CROSSREFS

Sequence in context: A079700 A357722 A374540 * A373387 A309913 A317905

Adjacent sequences: A135359 A135360 A135361 * A135363 A135364 A135365

KEYWORD

nonn

AUTHOR