Computing the dimensions of spaces of modular & cusp forms

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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 in [1..70]];

How can this sequence be computed with Sage?

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