Defining parameters
| Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 975.g (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 39 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(140\) | ||
| Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(975, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 20 | 11 | 9 |
| Cusp forms | 8 | 5 | 3 |
| Eisenstein series | 12 | 6 | 6 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 5 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(975, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 975.1.g.a | $1$ | $0.487$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) | \(\Q(\sqrt{13}) \) | \(0\) | \(1\) | \(0\) | \(0\) | \(q+q^{3}-q^{4}+q^{9}-q^{12}+q^{13}+q^{16}+\cdots\) |
| 975.1.g.b | $2$ | $0.487$ | \(\Q(\sqrt{2}) \) | $D_{4}$ | \(\Q(\sqrt{-39}) \) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q-\beta q^{2}-q^{3}+q^{4}+\beta q^{6}+q^{9}-\beta q^{11}+\cdots\) |
| 975.1.g.c | $2$ | $0.487$ | \(\Q(\sqrt{2}) \) | $D_{4}$ | \(\Q(\sqrt{-39}) \) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q-\beta q^{2}+q^{3}+q^{4}-\beta q^{6}+q^{9}+\beta q^{11}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(975, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(975, [\chi]) \cong \)