Defining parameters
Level: | \( N \) | \(=\) | \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 3600.ey (of order \(30\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 225 \) |
Character field: | \(\Q(\zeta_{30})\) | ||
Sturm bound: | \(2160\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(3600, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 11616 | 2896 | 8720 |
Cusp forms | 11424 | 2864 | 8560 |
Eisenstein series | 192 | 32 | 160 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(3600, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{3}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1800, [\chi])\)\(^{\oplus 2}\)