Defining parameters
Level: | \( N \) | \(=\) | \( 468 = 2^{2} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 468.bw (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 117 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(168\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(468, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 360 | 56 | 304 |
Cusp forms | 312 | 56 | 256 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(468, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
468.2.bw.a | $56$ | $3.737$ | None | \(0\) | \(0\) | \(0\) | \(-2\) |
Decomposition of \(S_{2}^{\mathrm{old}}(468, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(468, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 2}\)