Defining parameters
| Level: | \( N \) | \(=\) | \( 4212 = 2^{2} \cdot 3^{4} \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 4212.dh (of order \(27\) and degree \(18\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 81 \) |
| Character field: | \(\Q(\zeta_{27})\) | ||
| Sturm bound: | \(1512\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4212, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 13716 | 1944 | 11772 |
| Cusp forms | 13500 | 1944 | 11556 |
| Eisenstein series | 216 | 0 | 216 |
Decomposition of \(S_{2}^{\mathrm{new}}(4212, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(4212, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4212, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1053, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2106, [\chi])\)\(^{\oplus 2}\)