Defining parameters
Level: | \( N \) | \(=\) | \( 2592 = 2^{5} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2592.bd (of order \(18\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 216 \) |
Character field: | \(\Q(\zeta_{18})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(432\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2592, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 216 | 18 | 198 |
Cusp forms | 72 | 6 | 66 |
Eisenstein series | 144 | 12 | 132 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 6 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(2592, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
2592.1.bd.a | $6$ | $1.294$ | \(\Q(\zeta_{18})\) | $D_{9}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{18}^{6}+\zeta_{18}^{8})q^{11}+(\zeta_{18}-\zeta_{18}^{2}+\cdots)q^{17}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2592, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2592, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1296, [\chi])\)\(^{\oplus 2}\)