Defining parameters
| Level: | \( N \) | \(=\) | \( 8640 = 2^{6} \cdot 3^{3} \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8640.z (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 80 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(3456\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8640, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3552 | 384 | 3168 |
| Cusp forms | 3360 | 384 | 2976 |
| Eisenstein series | 192 | 0 | 192 |
Decomposition of \(S_{2}^{\mathrm{new}}(8640, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8640, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8640, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2160, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2880, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4320, [\chi])\)\(^{\oplus 2}\)