Defining parameters
Level: | \( N \) | \(=\) | \( 9072 = 2^{4} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9072.dk (of order \(9\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 27 \) |
Character field: | \(\Q(\zeta_{9})\) | ||
Sturm bound: | \(3456\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(9072, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 10584 | 648 | 9936 |
Cusp forms | 10152 | 648 | 9504 |
Eisenstein series | 432 | 0 | 432 |
Decomposition of \(S_{2}^{\mathrm{new}}(9072, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(9072, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(9072, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1134, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1296, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1512, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2268, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3024, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4536, [\chi])\)\(^{\oplus 2}\)