Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(2916, [\chi])\).
|
Total |
New |
Old |
Modular forms
| 1026 |
72 |
954 |
Cusp forms
| 918 |
72 |
846 |
Eisenstein series
| 108 |
0 |
108 |
\( S_{3}^{\mathrm{old}}(2916, [\chi]) \cong \)
\(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 10}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 12}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 8}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 9}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(243, [\chi])\)\(^{\oplus 6}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 3}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(486, [\chi])\)\(^{\oplus 4}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(729, [\chi])\)\(^{\oplus 3}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(972, [\chi])\)\(^{\oplus 2}\)\(\oplus\)
\(S_{3}^{\mathrm{new}}(1458, [\chi])\)\(^{\oplus 2}\)