Defining parameters
| Level: | \( N \) | \(=\) | \( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3900.cy (of order \(12\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 195 \) |
| Character field: | \(\Q(\zeta_{12})\) | ||
| Sturm bound: | \(1680\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3900, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3504 | 336 | 3168 |
| Cusp forms | 3216 | 336 | 2880 |
| Eisenstein series | 288 | 0 | 288 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(3900, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(3900, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1950, [\chi])\)\(^{\oplus 2}\)