Defining parameters
| Level: | \( N \) | \(=\) | \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3600.bb (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 80 \) |
| Character field: | \(\Q(i)\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(720\) | ||
| Trace bound: | \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3600, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 52 | 8 | 44 |
| Cusp forms | 4 | 4 | 0 |
| Eisenstein series | 48 | 4 | 44 |
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 \(S_{1}^{\mathrm{new}}(3600, [\chi])\) into newform subspaces
| Label | Dim. | \(A\) | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||||
| 3600.1.bb.a | \(2\) | \(1.797\) | \(\Q(\sqrt{-1}) \) | \(D_{4}\) | \(\Q(\sqrt{-15}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-iq^{2}-q^{4}+iq^{8}+q^{16}+(-1+i+\cdots)q^{17}+\cdots\) |
| 3600.1.bb.b | \(2\) | \(1.797\) | \(\Q(\sqrt{-1}) \) | \(D_{4}\) | \(\Q(\sqrt{-15}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{2}-q^{4}-iq^{8}+q^{16}+(1-i+\cdots)q^{17}+\cdots\) |