Defining parameters
| Level: | \( N \) | \(=\) | \( 1536 = 2^{9} \cdot 3 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1536.h (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 24 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(256\) | ||
| Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1536, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 54 | 8 | 46 |
| Cusp forms | 22 | 8 | 14 |
| Eisenstein series | 32 | 0 | 32 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 8 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1536, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 1536.1.h.a | $2$ | $0.767$ | \(\Q(\sqrt{2}) \) | $D_{4}$ | \(\Q(\sqrt{-6}) \) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q-q^{3}-\beta q^{5}-\beta q^{7}+q^{9}+\beta q^{15}+\cdots\) |
| 1536.1.h.b | $2$ | $0.767$ | \(\Q(\sqrt{2}) \) | $D_{4}$ | \(\Q(\sqrt{-6}) \) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+q^{3}-\beta q^{5}+\beta q^{7}+q^{9}-\beta q^{15}+\cdots\) |
| 1536.1.h.c | $4$ | $0.767$ | \(\Q(\zeta_{8})\) | $D_{4}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{9}+(-\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1536, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1536, [\chi]) \cong \)