Defining parameters
Level: | \( N \) | \(=\) | \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1872.fn (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 39 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Sturm bound: | \(1344\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1872, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 4128 | 336 | 3792 |
Cusp forms | 3936 | 336 | 3600 |
Eisenstein series | 192 | 0 | 192 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1872, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(1872, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1872, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(936, [\chi])\)\(^{\oplus 2}\)