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2 | 2 | Design notes
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3 | 3 |
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4 | 4 | The implementation depends on the fact that we have dimension formulas
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5 |
| -(see `dims.py`) for spaces of modular forms with character, and new |
| 5 | +(see ``dims.py``) for spaces of modular forms with character, and new |
6 | 6 | subspaces, so that we don't have to compute `q`-expansions for the whole
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7 | 7 | space in order to compute `q`-expansions / elements / and dimensions of
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8 | 8 | certain subspaces. Also, the following design is much simpler than
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12 | 12 | else.
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13 | 13 |
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14 | 14 | The internal basis of `q`-expansions of modular forms for the ambient
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15 |
| -space is defined as follows: |
| 15 | +space is defined as follows:: |
16 | 16 |
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17 | 17 | First Block: Cuspidal Subspace
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18 | 18 | Second Block: Eisenstein Subspace
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19 | 19 |
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20 |
| - Cuspidal Subspace: Block for each level M dividing N, from highest |
21 |
| - level to lowest. The block for level M |
22 |
| - contains the images at level N of the |
23 |
| - newsubspace of level M (basis, then |
| 20 | + Cuspidal Subspace: Block for each level `M` dividing `N`, from highest |
| 21 | + level to lowest. The block for level `M` |
| 22 | + contains the images at level `N` of the |
| 23 | + newsubspace of level `M` (basis, then |
24 | 24 | basis(q**d), then basis(q**e), etc.)
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25 | 25 |
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26 | 26 | Eisenstein Subspace: characters, etc.
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