Defining parameters
| Level: | \( N \) | \(=\) | \( 4100 = 2^{2} \cdot 5^{2} \cdot 41 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 4100.gx (of order \(40\) and degree \(16\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 205 \) |
| Character field: | \(\Q(\zeta_{40})\) | ||
| Sturm bound: | \(1260\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4100, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 10368 | 1008 | 9360 |
| Cusp forms | 9792 | 1008 | 8784 |
| Eisenstein series | 576 | 0 | 576 |
Decomposition of \(S_{2}^{\mathrm{new}}(4100, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(4100, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(205, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(410, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(820, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1025, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2050, [\chi])\)\(^{\oplus 2}\)