Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(684, [\chi])\).
|
Total |
New |
Old |
Modular forms
| 492 |
24 |
468 |
Cusp forms
| 468 |
24 |
444 |
Eisenstein series
| 24 |
0 |
24 |
\( S_{5}^{\mathrm{old}}(684, [\chi]) \cong \)
\(S_{5}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 8}\)\(\oplus\)
\(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{5}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{5}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{5}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)
\(S_{5}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{5}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{5}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 3}\)\(\oplus\)
\(S_{5}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)\(\oplus\)
\(S_{5}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)