Defining parameters
| Level: | \( N \) | \(=\) | \( 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 4900.ci (of order \(42\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 245 \) |
| Character field: | \(\Q(\zeta_{42})\) | ||
| Sturm bound: | \(1680\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4900, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 10296 | 1008 | 9288 |
| Cusp forms | 9864 | 1008 | 8856 |
| Eisenstein series | 432 | 0 | 432 |
Decomposition of \(S_{2}^{\mathrm{new}}(4900, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(4900, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2450, [\chi])\)\(^{\oplus 2}\)