Defining parameters
Level: | \( N \) | \(=\) | \( 77 = 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 77.j (of order \(10\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 77 \) |
Character field: | \(\Q(\zeta_{10})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(8\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(77, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 12 | 12 | 0 |
Cusp forms | 4 | 4 | 0 |
Eisenstein series | 8 | 8 | 0 |
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 \(S_{1}^{\mathrm{new}}(77, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
77.1.j.a | $4$ | $0.038$ | \(\Q(\zeta_{10})\) | $D_{5}$ | \(\Q(\sqrt{-7}) \) | None | \(-2\) | \(0\) | \(0\) | \(-1\) | \(q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots\) |