Defining parameters
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.l (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 45 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 15 \) | ||
Sturm bound: | \(162\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(405, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 480 | 200 | 280 |
Cusp forms | 384 | 184 | 200 |
Eisenstein series | 96 | 16 | 80 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(405, [\chi])\) into newform subspaces
Decomposition of \(S_{3}^{\mathrm{old}}(405, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(405, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)