Defining parameters
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(960, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 36 | 8 | 28 |
Cusp forms | 12 | 4 | 8 |
Eisenstein series | 24 | 4 | 20 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(960, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
960.1.c.a | $4$ | $0.479$ | \(\Q(\zeta_{8})\) | $D_{4}$ | \(\Q(\sqrt{-5}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{5}+(\zeta_{8}+\zeta_{8}^{3})q^{7}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(960, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)