Defining parameters
| Level: | \( N \) | \(=\) | \( 38025 = 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 38025.de (of order \(12\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 39 \) |
| Character field: | \(\Q(\zeta_{12})\) | ||
| Sturm bound: | \(10920\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(38025, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 22512 | 3904 | 18608 |
| Cusp forms | 21168 | 3904 | 17264 |
| Eisenstein series | 1344 | 0 | 1344 |
Decomposition of \(S_{2}^{\mathrm{new}}(38025, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(38025, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(38025, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1521, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2535, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2925, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(7605, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(12675, [\chi])\)\(^{\oplus 2}\)