Defining parameters
| Level: | \( N \) | \(=\) | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 980.p (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 140 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(168\) | ||
| Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(980, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 52 | 28 | 24 |
| Cusp forms | 20 | 12 | 8 |
| Eisenstein series | 32 | 16 | 16 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 12 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(980, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 980.1.p.a | $2$ | $0.489$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-5}) \) | None | \(-1\) | \(-1\) | \(1\) | \(0\) | \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots\) |
| 980.1.p.b | $2$ | $0.489$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-5}) \) | None | \(1\) | \(1\) | \(1\) | \(0\) | \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots\) |
| 980.1.p.c | $8$ | $0.489$ | \(\Q(\zeta_{24})\) | $D_{4}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}-\zeta_{24}^{7}q^{5}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(980, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(980, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)