Transcript below. Ironically, no error is produced by the related
command
sage: time f=D[6].q_eigenform(7,'a')
rje
*************************************************************************************************
rev...@sobolev:~% sage
----------------------------------------------------------------------
| Sage Version 3.4.2, Release Date: 2009-05-05 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: time G=DirichletGroup(525,CyclotomicField(4));X=G.list();Y=X
[15];
M=ModularSymbols(Y,3,sign=1)
CPU times: user 94.43 s, sys: 0.10 s, total: 94.53 s
Wall time: 94.52 s
sage: M
Modular Symbols space of dimension 160 and level 525, weight 3,
character
[-1, -zeta4, -1], sign 1, over Cyclotomic Field of order 4 and degree
2
sage: time D=M.cuspidal_subspace().new_subspace().decomposition()
CPU times: user 6833.46 s, sys: 303.90 s, total: 7137.37 s
Wall time: 7136.81 s
sage: D
[
Modular Symbols subspace of dimension 2 of Modular Symbols space of
dimension 160 and level 525, weight 3, character [-1, -zeta4, -1],
sign 1,
over Cyclotomic Field of order 4 and degree 2,
Modular Symbols subspace of dimension 2 of Modular Symbols space of
dimension 160 and level 525, weight 3, character [-1, -zeta4, -1],
sign 1,
over Cyclotomic Field of order 4 and degree 2,
Modular Symbols subspace of dimension 4 of Modular Symbols space of
dimension 160 and level 525, weight 3, character [-1, -zeta4, -1],
sign 1,
over Cyclotomic Field of order 4 and degree 2,
Modular Symbols subspace of dimension 4 of Modular Symbols space of
dimension 160 and level 525, weight 3, character [-1, -zeta4, -1],
sign 1,
over Cyclotomic Field of order 4 and degree 2,
Modular Symbols subspace of dimension 4 of Modular Symbols space of
dimension 160 and level 525, weight 3, character [-1, -zeta4, -1],
sign 1,
over Cyclotomic Field of order 4 and degree 2,
Modular Symbols subspace of dimension 4 of Modular Symbols space of
dimension 160 and level 525, weight 3, character [-1, -zeta4, -1],
sign 1,
over Cyclotomic Field of order 4 and degree 2,
Modular Symbols subspace of dimension 8 of Modular Symbols space of
dimension 160 and level 525, weight 3, character [-1, -zeta4, -1],
sign 1,
over Cyclotomic Field of order 4 and degree 2,
Modular Symbols subspace of dimension 8 of Modular Symbols space of
dimension 160 and level 525, weight 3, character [-1, -zeta4, -1],
sign 1,
over Cyclotomic Field of order 4 and degree 2,
Modular Symbols subspace of dimension 16 of Modular Symbols space of
dimension 160 and level 525, weight 3, character [-1, -zeta4, -1],
sign 1,
over Cyclotomic Field of order 4 and degree 2,
Modular Symbols subspace of dimension 40 of Modular Symbols space of
dimension 160 and level 525, weight 3, character [-1, -zeta4, -1],
sign 1,
over Cyclotomic Field of order 4 and degree 2
]
sage: time f=D[4].q_eigenform(7,'a') #HERE IS THE OFFENDING
COMMAND
---------------------------------------------------------------------------
IndexError Traceback (most recent call
last)
/base/people/revans/<ipython console> in <module>()
/usr/local/sage/local/lib/python2.5/site-packages/IPython/iplib.pyc
in
ipmagic(self, arg_s)
951 else:
952 magic_args = self.var_expand(magic_args,1)
--> 953 return fn(magic_args)
954
955 def ipalias(self,arg_s):
/usr/local/sage/local/lib/python2.5/site-packages/IPython/Magic.pyc
in
magic_time(self, parameter_s)
1909 else:
1910 st = clk()
-> 1911 exec code in glob
1912 end = clk()
1913 out = None
/base/people/revans/<timed exec> in <module>()
/usr/local/sage/local/lib/python2.5/site-packages/sage/modular/modsym/
space.pyc
in q_eigenform(self, prec, names)
1077 return
self.plus_submodule(compute_dual=True).q_eigenform(prec, names)
1078 raise ArithmeticError, "self must be simple."
-> 1079 a2 = self.eigenvalue(2, names)
1080 R = PowerSeriesRing(a2.parent(), "q")
1081 q = R.gen(0)
/usr/local/sage/local/lib/python2.5/site-packages/sage/modular/hecke/
module.pyc
in eigenvalue(self, n, name)
907
908 if (arith.is_prime(n) or n==1):
--> 909 Tn_e = self._eigen_nonzero_element(n)
910 an = self._element_eigenvalue(Tn_e, name=name)
911 dict_set(ev, n, name, an)
/usr/local/sage/local/lib/python2.5/site-packages/sage/modular/hecke/
module.pyc
in _eigen_nonzero_element(self, n)
394 raise ArithmeticError, "the rank of self must be
positive"
395 A = self.ambient_hecke_module()
--> 396 i = self._eigen_nonzero()
397 return A._hecke_image_of_ith_basis_vector(n, i)
398
/usr/local/sage/local/lib/python2.5/site-packages/sage/modular/hecke/
module.pyc
in _eigen_nonzero(self)
375 pass
376 A = self.ambient_hecke_module()
--> 377 V = self.dual_free_module()
378 B = V.basis()
379 for i in range(V.degree()):
/usr/local/sage/local/lib/python2.5/site-packages/sage/modular/hecke/
submodule.pyc
in dual_free_module(self, bound, anemic, use_star)
401 f = self.hecke_polynomial(p)
402 T = A.dual_hecke_matrix(p)
--> 403 V = T.kernel_on(V, poly=f, check=False)
404 if V.dimension() <= self.dimension():
405 break
/usr/local/sage/local/lib/python2.5/site-packages/sage/matrix/
matrix2.so in
sage.matrix.matrix2.Matrix.kernel_on (sage/matrix/matrix2.c:11763)()
/usr/local/sage/local/lib/python2.5/site-packages/sage/rings/
polynomial/polynomial_element.so
in sage.rings.polynomial.polynomial_element.Polynomial.__call__
(sage/rings/polynomial/polynomial_element.c:6824)()
/usr/local/sage/local/lib/python2.5/site-packages/sage/rings/
polynomial/polynomial_compiled.so
in
sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval
(sage/rings/polynomial/polynomial_compiled.c:1254)()
/usr/local/sage/local/lib/python2.5/site-packages/sage/rings/
polynomial/polynomial_compiled.so
in sage.rings.polynomial.polynomial_compiled.pd_eval
(sage/rings/polynomial/polynomial_compiled.c:2296)()
/usr/local/sage/local/lib/python2.5/site-packages/sage/rings/
polynomial/polynomial_compiled.so
in sage.rings.polynomial.polynomial_compiled.mul_pd.eval
(sage/rings/polynomial/polynomial_compiled.c:4111)()
/usr/local/sage/local/lib/python2.5/site-packages/sage/rings/
polynomial/polynomial_compiled.so
in sage.rings.polynomial.polynomial_compiled.pd_eval
(sage/rings/polynomial/polynomial_compiled.c:2296)()
/usr/local/sage/local/lib/python2.5/site-packages/sage/rings/
polynomial/polynomial_compiled.so
in sage.rings.polynomial.polynomial_compiled.sqr_pd.eval
(sage/rings/polynomial/polynomial_compiled.c:3378)()
/usr/local/sage/local/lib/python2.5/site-packages/sage/rings/
polynomial/polynomial_compiled.so
in sage.rings.polynomial.polynomial_compiled.pd_eval
(sage/rings/polynomial/polynomial_compiled.c:2296)()
/usr/local/sage/local/lib/python2.5/site-packages/sage/rings/
polynomial/polynomial_compiled.so
in sage.rings.polynomial.polynomial_compiled.sqr_pd.eval
(sage/rings/polynomial/polynomial_compiled.c:3389)()
/usr/local/sage/local/lib/python2.5/site-packages/sage/structure/
element.so
in sage.structure.element.Matrix.__mul__ (sage/structure/element.c:
12803)()
/usr/local/sage/local/lib/python2.5/site-packages/sage/matrix/
matrix_cyclo_dense.so
in
sage.matrix.matrix_cyclo_dense.Matrix_cyclo_dense._matrix_times_matrix_
(sage/matrix/matrix_cyclo_dense.cpp:6167)()
/usr/local/sage/local/lib/python2.5/site-packages/sage/matrix/
matrix_integer_dense.so
in sage.matrix.matrix_integer_dense._lift_crt
(sage/matrix/matrix_integer_dense.c:35969)()
IndexError: list index out of range
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