Changes between Version 1 and Version 2 of Ticket #17283


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Timestamp:
11/04/14 20:52:32 (5 years ago)
Author:
pbruin
Comment:

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  • Ticket #17283

    • Property Keywords dirichlet character added; dimension removed
    • Property Summary changed from Dimension mismatch in cuspidal_submodule() to Changing the coefficient ring of a Dirichlet character gives a wrong result
  • Ticket #17283 – Description

    v1 v2  
    1 In the following example, two ways of computing the dimension of a space of modular symbols do not give the same result:
     1Changing the coefficient field of a Dirichlet character is broken in some cases (the conductor and the image of 133 are wrong in `chi0`):
    22{{{
    3 sage: k.<i> = QuadraticField(-1)
     3sage: k.<i> = CyclotomicField(4)
    44sage: G = DirichletGroup(192)
    5 sage: chi = G([i,-1,-1])
     5sage: G0 = DirichletGroup(192, k)
     6sage: chi = G([i,-1,-1]); chi
     7Dirichlet character modulo 192 of conductor 48 mapping 127 |--> zeta16^4, 133 |--> -1, 65 |--> -1
     8sage: chi0 = G0(chi); chi0
     9Dirichlet character modulo 192 of conductor 24 mapping 127 |--> i, 133 |--> 1, 65 |--> -1
     10}}}
     11
     12This probably explains the following bug where two ways of computing the dimension of a space of modular symbols do not give the same result:
     13{{{
    614sage: M = ModularSymbols(chi);
    715sage: M.cuspidal_submodule()
    816AssertionError: According to dimension formulas the cuspidal subspace of "Modular Symbols space of dimension 0 and level 192, weight 2, character [zeta4, 1, -1], sign 0, over Cyclotomic Field of order 4 and degree 2" has dimension 40; however, computing it using modular symbols we obtained 0, so there is a bug (please report!).
    917}}}
    10 The following problem is probably related (the conductor and the image of 133 are wrong in `M.character()`):
    11 {{{
    12 sage: chi
    13 Dirichlet character modulo 192 of conductor 48 mapping 127 |--> zeta16^4, 133 |--> -1, 65 |--> -1
    14 sage: M.character()
    15 Dirichlet character modulo 192 of conductor 24 mapping 127 |--> zeta4, 133 |--> 1, 65 |--> -1
    16 }}}
     18