Defining parameters
| Level: | \( N \) | \(=\) | \( 1984 = 2^{6} \cdot 31 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1984.bk (of order \(15\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 31 \) |
| Character field: | \(\Q(\zeta_{15})\) | ||
| Sturm bound: | \(512\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1984, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2144 | 528 | 1616 |
| Cusp forms | 1952 | 496 | 1456 |
| Eisenstein series | 192 | 32 | 160 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1984, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(1984, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1984, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(124, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(248, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(496, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(992, [\chi])\)\(^{\oplus 2}\)