Defining parameters
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 24 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1728, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 58 | 4 | 54 |
Cusp forms | 22 | 4 | 18 |
Eisenstein series | 36 | 0 | 36 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1728, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1728.1.h.a | $4$ | $0.862$ | \(\Q(\zeta_{12})\) | $D_{6}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{12}-\zeta_{12}^{5})q^{7}+(-\zeta_{12}^{2}-\zeta_{12}^{4}+\cdots)q^{13}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1728, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1728, [\chi]) \cong \)