Changes between Version 3 and Version 4 of Ticket #17283
 Timestamp:
 11/11/14 21:35:06 (5 years ago)
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Ticket #17283
 Property Keywords modular symbols removed

Property
Priority
changed from
critical
tominor

Property
Summary
changed from
Evaluating Dirichlet characters can give wrong results
toCheck consistency when constructing Dirichlet characters

Ticket #17283 – Description
v3 v4 1 Evaluating Dirichlet characters is broken in some cases (the image of 133 is wrong in this example):1 It is too easy to construct Dirichlet characters with inconsistent values: 2 2 {{{ 3 3 sage: k.<i> = CyclotomicField(4) 4 4 sage: G = DirichletGroup(192) 5 sage: chi = G([i,1,1]); chi 5 sage: chi = G([i,1,1]); chi # should raise an error since 127 only has order 2 6 6 Dirichlet character modulo 192 of conductor 48 mapping 127 > zeta16^4, 133 > 1, 65 > 1 7 sage: chi(133) 7 sage: chi(133) # no surprise that this gives an inconsistent answer 8 8 1 9 9 }}} 10 Because of this, changing the coefficient field of `chi` is broken as well: 11 {{{ 12 sage: G0 = DirichletGroup(192, k) 13 sage: chi0 = G0(chi); chi0 14 Dirichlet character modulo 192 of conductor 24 mapping 127 > i, 133 > 1, 65 > 1 15 }}} 16 17 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: 18 {{{ 19 sage: M = ModularSymbols(chi); 20 sage: M.cuspidal_submodule() 21 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!). 22 }}} 23 10 The `check` option (`True` by default) should verify that the images of the generators have the correct orders.