Defining parameters
Level: | \( N \) | \(=\) | \( 32 = 2^{5} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 32.g (of order \(8\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 32 \) |
Character field: | \(\Q(\zeta_{8})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(32\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(32, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 116 | 116 | 0 |
Cusp forms | 108 | 108 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(32, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
32.8.g.a | $108$ | $9.996$ | None | \(-4\) | \(-4\) | \(-4\) | \(-4\) |