Sharedwww / ono / apmod_run28.gpOpen in CoCalc
Author: William A. Stein
1\\apmod_run28.gp
2\\Compute Hecke eigenvalues for a basis of newforms of
3\\S_k(Gamma_0(N); Fp).  This is really computed using modular symbols
4\\so in some special cases the computation may fail, e.g., maybe, if p divides
5\\the discriminant of the Hecke algebra.
6\\It is also possible, but very unlikely if p>3, that the dimension
7\\of the modp reduction will go up because of "spurious torsion."
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9\\ Notation: This table is destined to be input into PARI.
10\\ Unfortunately, PARI doesn't support n-dimensional arrays.
11\\ Thus for now the output format is
12\\    apmod_k7p13[N,i] = [g(x), [a2(x), a3(x), a5(x), ...]].
13\\ where k=7,p=13 are examples,
14\\ i is the conjugacy class (in no particular order),
15\\ g(x) is an irreducible poly over Fp, and the Hecke eigenvalues a2, a3, ...
16\\ are expressed as polynomials in a fixed root of g(x).
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18\\ William Stein ([email protected])
19\\ Fri May 21 23:22:38 1999
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