Defining parameters
Level: | \( N \) | \(=\) | \( 961 = 31^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 961.h (of order \(30\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 31 \) |
Character field: | \(\Q(\zeta_{30})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(82\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(961, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 136 | 120 | 16 |
Cusp forms | 8 | 8 | 0 |
Eisenstein series | 128 | 112 | 16 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 8 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(961, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
961.1.h.a | $8$ | $0.480$ | \(\Q(\zeta_{15})\) | $D_{3}$ | \(\Q(\sqrt{-31}) \) | None | \(2\) | \(0\) | \(4\) | \(-1\) | \(q+\zeta_{30}^{3}q^{2}-\zeta_{30}^{10}q^{5}+\zeta_{30}^{11}q^{7}+\cdots\) |