Defining parameters
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 197.c (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 197 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(49\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(197, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 68 | 68 | 0 |
Cusp forms | 64 | 64 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(197, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
197.3.c.a | $64$ | $5.368$ | None | \(-2\) | \(-2\) | \(-10\) | \(0\) |