Dear William,
I thank you for your very prompt replay!
Actually ther is a missprint in my post: the my group
is Gamma0(15), not Gamma0(11), so the first line of
my code was
SAGE: chi=DirichletGroup(15,QQ).1
so that the dimension of the eigenforms space is 4.
I have just tried the code on the public notebook server
without any crash: as you suggest me the origin of my
problem is evidently in my binary (I'm using windows
with VMware Player). In next days I will download a
different version.
Thank you again,
Beppe
William Stein ha scritto:
On Fri, Feb 6, 2009 at 8:58 AM, beppe giuseppe.molt...@gmail.com wrote:
Hello,
I'm novice in SAGE but I have a strange problem:
I have to compute some eigenvalues for the set of cuspidal newforms
for the group Gamma0(15), weight 4 and Legendre character chi of
conductor 5, so I type in SAGE the following set of instruction:
SAGE: chi=DirichletGroup(11,QQ).1
SAGE: m=numerical_eigenforms(chi,4); m
Numerical Hecke eigenvalues for [1,-1] of weight 4
SAGE: m.ap(2)
This instruction produces a crash: in notebook the system answers:
/usr/local/sage/local/bin/sage-sage: line 352: 4080 Illegal
instruction
python $@
In SAGE command line mode this set of instructions produces a similar
crash.
Some could help me? I thank you in advance,
Beppe
You downloaded the wrong binary. Fixes:
(1) download the right binary, if there is one available, or
(2) use the public sage notebook server (sagenb.org), or
(3) build sage from source.
Second your code contains a bug:
chi=DirichletGroup(11,QQ).1
should be
chi=DirichletGroup(11,QQ).0
since the indexing in sage is 0 based.
Third, that space as dimension 0. But if you
chi=DirichletGroup(11,QQ).0^2
you get something of dimension 4.
Here's some examples of how things were when you have a binary for the
right machine:
sage: chi=DirichletGroup(11,QQ).0^2
sage: m=numerical_eigenforms(chi,4); m
sage: m.ap(2)
[9.0, 9.0 + 2.77555756156e-17*I, 2.73205080757 + 1.23504195035e-16*I,
-0.732050807569 - 2.08519811694e-15*I]
sage: dimension_modular_forms(chi^2,4)
4
sage: m.ap(3)
[28.0, 28.0 - 1.66533453694e-16*I, -7.92820323028 +
3.91694614232e-15*I, 5.92820323028 - 5.96234312405e-16*I]
sage: ModularForms(chi,4)
Modular Forms space of dimension 4 for Congruence Subgroup Gamma0(11)
of weight 4 over Rational Field
sage: ModularForms(chi,4).basis()
[
q + 3*q^3 - 6*q^4 - 7*q^5 + O(q^6),
q^2 - 4*q^3 + 2*q^4 + 8*q^5 + O(q^6),
1 + O(q^6),
q + 9*q^2 + 28*q^3 + 73*q^4 + 126*q^5 + O(q^6)
]
-- William
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