Changes between Version 1 and Version 2 of Ticket #17283
 Timestamp:
 11/04/14 20:52:32 (5 years ago)
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Ticket #17283
 Property Keywords dirichlet character added; dimension removed

Property
Summary
changed from
Dimension mismatch in cuspidal_submodule()
toChanging 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:1 Changing the coefficient field of a Dirichlet character is broken in some cases (the conductor and the image of 133 are wrong in `chi0`): 2 2 {{{ 3 sage: k.<i> = QuadraticField(1)3 sage: k.<i> = CyclotomicField(4) 4 4 sage: G = DirichletGroup(192) 5 sage: chi = G([i,1,1]) 5 sage: G0 = DirichletGroup(192, k) 6 sage: chi = G([i,1,1]); chi 7 Dirichlet character modulo 192 of conductor 48 mapping 127 > zeta16^4, 133 > 1, 65 > 1 8 sage: chi0 = G0(chi); chi0 9 Dirichlet character modulo 192 of conductor 24 mapping 127 > i, 133 > 1, 65 > 1 10 }}} 11 12 This 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 {{{ 6 14 sage: M = ModularSymbols(chi); 7 15 sage: M.cuspidal_submodule() 8 16 AssertionError: 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!). 9 17 }}} 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