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The first thing to try is:

sage: Q.basis()
[
(1, 0),
(0, 1)
]

but as you can see, it returns a basis within itself, not within $V$. So what you have to do is to lift each element of that basis into $V$:

sage: [Q.lift(b) for b in Q.basis()]
[(1, 0, 0, 0), (0, 0, 1, -7/5)]

If you prefer, you can make this basis a matrix as follows:

sage: matrix([Q.lift(b) for b in Q.basis()])
[   1    0    0    0]
[   0    0    1 -7/5]

The Let me first give a name to the quotient $V/W$:

sage: Q = V/W

Now, searching within the avaiable methods, the first thing to try is:

sage: Q.basis()
[
(1, 0),
(0, 1)
]

but as you can see, it returns a basis within itself, not within $V$. So what you have to do is to lift each element of that basis into $V$:

sage: [Q.lift(b) for b in Q.basis()]
[(1, 0, 0, 0), (0, 0, 1, -7/5)]

If you prefer, you can make this basis a matrix as follows:

sage: matrix([Q.lift(b) for b in Q.basis()])
[   1    0    0    0]
[   0    0    1 -7/5]