Defining parameters
| Level: | \( N \) | \(=\) | \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1872.fi (of order \(12\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 117 \) |
| Character field: | \(\Q(\zeta_{12})\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(336\) | ||
| Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1872, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 72 | 16 | 56 |
| Cusp forms | 24 | 8 | 16 |
| Eisenstein series | 48 | 8 | 40 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 0 | 0 | 8 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1872, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 1872.1.fi.a | $4$ | $0.934$ | \(\Q(\zeta_{12})\) | $S_{4}$ | None | None | \(0\) | \(-2\) | \(2\) | \(0\) | \(q-\zeta_{12}^{2}q^{3}+(\zeta_{12}^{2}-\zeta_{12}^{5})q^{5}+\zeta_{12}^{4}q^{9}+\cdots\) |
| 1872.1.fi.b | $4$ | $0.934$ | \(\Q(\zeta_{12})\) | $S_{4}$ | None | None | \(0\) | \(2\) | \(0\) | \(2\) | \(q+\zeta_{12}^{2}q^{3}+(\zeta_{12}-\zeta_{12}^{4})q^{7}+\zeta_{12}^{4}q^{9}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1872, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1872, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(936, [\chi])\)\(^{\oplus 2}\)