Defining parameters
| Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 2160.c (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(432\) | ||
| Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2160, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 60 | 6 | 54 |
| Cusp forms | 24 | 6 | 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 | 2 | 0 | 4 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(2160, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 2160.1.c.a | $1$ | $1.078$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-15}) \) | None | \(0\) | \(0\) | \(-1\) | \(0\) | \(q-q^{5}+q^{17}+q^{19}-q^{23}+q^{25}+\cdots\) |
| 2160.1.c.b | $1$ | $1.078$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-15}) \) | None | \(0\) | \(0\) | \(1\) | \(0\) | \(q+q^{5}-q^{17}+q^{19}+q^{23}+q^{25}+\cdots\) |
| 2160.1.c.c | $4$ | $1.078$ | \(\Q(\zeta_{8})\) | $S_{4}$ | None | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{7}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2160, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2160, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)