Defining parameters
Level: | \( N \) | \(=\) | \( 810 = 2 \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 810.m (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 45 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Sturm bound: | \(648\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(810, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2040 | 288 | 1752 |
Cusp forms | 1848 | 288 | 1560 |
Eisenstein series | 192 | 0 | 192 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(810, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(810, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(810, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 2}\)