Defining parameters
| Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1950.bt (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 \(M_{4}(1950, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 5136 | 1008 | 4128 |
| Cusp forms | 4944 | 1008 | 3936 |
| Eisenstein series | 192 | 0 | 192 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1950, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(1950, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1950, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 2}\)