Defining parameters
Level: | \( N \) | \(=\) | \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1584.cb (of order \(10\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 132 \) |
Character field: | \(\Q(\zeta_{10})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(576\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1584, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1248 | 96 | 1152 |
Cusp forms | 1056 | 96 | 960 |
Eisenstein series | 192 | 0 | 192 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1584, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1584.2.cb.a | $32$ | $12.648$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
1584.2.cb.b | $64$ | $12.648$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1584, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1584, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 2}\)