Defining parameters
| Level: | \( N \) | \(=\) | \( 3712 = 2^{7} \cdot 29 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3712.u (of order \(7\) and degree \(6\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 29 \) |
| Character field: | \(\Q(\zeta_{7})\) | ||
| Sturm bound: | \(960\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3712, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2976 | 720 | 2256 |
| Cusp forms | 2784 | 720 | 2064 |
| Eisenstein series | 192 | 0 | 192 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(3712, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(3712, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3712, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(232, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(464, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(928, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1856, [\chi])\)\(^{\oplus 2}\)