Defining parameters
| Level: | \( N \) | \(=\) | \( 1359 = 3^{2} \cdot 151 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1359.d (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 151 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(152\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1359, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 23 | 11 | 12 |
| Cusp forms | 19 | 10 | 9 |
| Eisenstein series | 4 | 1 | 3 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 10 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1359, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 1359.1.d.a | $1$ | $0.678$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-151}) \) | \(\Q(\sqrt{453}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-q^{4}+q^{16}+2q^{19}-q^{25}+2q^{31}+\cdots\) |
| 1359.1.d.b | $3$ | $0.678$ | \(\Q(\zeta_{14})^+\) | $D_{7}$ | \(\Q(\sqrt{-151}) \) | None | \(1\) | \(0\) | \(1\) | \(0\) | \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\) |
| 1359.1.d.c | $6$ | $0.678$ | \(\Q(\zeta_{28})^+\) | $D_{14}$ | \(\Q(\sqrt{-151}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{8}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1359, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1359, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(151, [\chi])\)\(^{\oplus 3}\)