Defining parameters
| Level: | \( N \) | \(=\) | \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 7800.mb (of order \(60\) and degree \(16\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 325 \) |
| Character field: | \(\Q(\zeta_{60})\) | ||
| Sturm bound: | \(3360\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(7800, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 27136 | 3360 | 23776 |
| Cusp forms | 26624 | 3360 | 23264 |
| Eisenstein series | 512 | 0 | 512 |
Decomposition of \(S_{2}^{\mathrm{new}}(7800, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(7800, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(7800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1300, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1950, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2600, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3900, [\chi])\)\(^{\oplus 2}\)