### Computing the dimensions of spaces of modular & cusp forms

In OEIS A159634 Steven Finch gave the following
MAGMA snippet to compute the

*coefficient for dimensions of spaces of modular & cusp forms of weight k/2, level 4n and trivial character, where k >= 5 is odd.*

```
[[4*n, (Dimension(HalfIntegralWeightForms(4*n, 7/2)) +
Dimension(CuspidalSubspace(HalfIntegralWeightForms(4*n,
```~~5/2))))/2] : n ~~5/2))))/2]:n in [1..70]];

*How can this sequence be computed with Sage?*

Note that this question is related to a conjecture of Enrique Pérez Herrero.