Defining parameters
| Level: | \( N \) | \(=\) | \( 39326 = 2 \cdot 7 \cdot 53^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 39326.m (of order \(13\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 53 \) |
| Character field: | \(\Q(\zeta_{13})\) | ||
| Sturm bound: | \(11448\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(39326, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 69984 | 16536 | 53448 |
| Cusp forms | 67392 | 16536 | 50856 |
| Eisenstein series | 2592 | 0 | 2592 |
Decomposition of \(S_{2}^{\mathrm{new}}(39326, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(39326, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(39326, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(53, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(106, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(371, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(742, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2809, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(5618, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(19663, [\chi])\)\(^{\oplus 2}\)