Defining parameters
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.r (of order \(36\) and degree \(12\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 135 \) |
Character field: | \(\Q(\zeta_{36})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(108\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(405, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 720 | 240 | 480 |
Cusp forms | 576 | 192 | 384 |
Eisenstein series | 144 | 48 | 96 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(405, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
405.2.r.a | $192$ | $3.234$ | None | \(12\) | \(0\) | \(12\) | \(-12\) |
Decomposition of \(S_{2}^{\mathrm{old}}(405, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(405, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)