1 | initial version |

The character is determined by the two values on (the classes of) $15$ and $17$. The first element has a clear image, the second one...

```
sage: R.<X> = QQ[]
sage: K.<a> = NumberField( X^4 + 2*X^3 + 2*X^2 + 4*X + 4 )
sage: b = ( -a^3/2 - a^2/2 - a - 1 )
sage: b.minpoly()
x^2 - x + 1
sage: b^3
-1
sage: b^6
1
```

goes to a primitive 6th root of unity. This is enough to identify the character, up to conjugation.
The following code creates *one* of the two spaces of modular symbols related to the question:

```
sage: D28 = DirichletGroup( 28 )
sage: D28.order()
12
sage: D28.0
Dirichlet character modulo 28 of conductor 4 mapping 15 |--> -1, 17 |--> 1
sage: D28.1
Dirichlet character modulo 28 of conductor 7 mapping 15 |--> 1, 17 |--> zeta6
sage: ch = D28.0 * D28.1
sage: ch
Dirichlet character modulo 28 of conductor 28 mapping 15 |--> -1, 17 |--> zeta6
sage: MS = ModularSymbols( ch, 2, 1 )
sage: MS
Modular Symbols space of dimension 4 and level 28, weight 2, character [-1, zeta6], sign 1, over Cyclotomic Field of order 6 and degree 2
```

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.