Defining parameters
| Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 576.b (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(96\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(576, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 26 | 2 | 24 |
| Cusp forms | 2 | 2 | 0 |
| Eisenstein series | 24 | 0 | 24 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 2 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(576, [\chi])\) into newform subspaces
| Label | Dim. | \(A\) | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 576.1.b.a | $2$ | $0.287$ | \(\Q(\sqrt{-1}) \) | $D_{2}$ | \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-6}) \) | \(\Q(\sqrt{2}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-iq^{7}+q^{25}+iq^{31}-3q^{49}-q^{73}+\cdots\) |