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

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

Jonathan Vos Post, Feb 16 2008

Extensions

Terms a(106)..a(167) from Klaus Brockhaus, Feb 19 2008

Terms a(168)..a(209) from Jason Kimberley, Oct 07 2012

Status

approved