Defining parameters
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.c (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 29 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(7\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(29, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 12 | 12 | 0 |
Cusp forms | 8 | 8 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(29, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
29.3.c.a | $8$ | $0.790$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(2\) | \(-2\) | \(0\) | \(-4\) | \(q-\beta _{6}q^{2}+(\beta _{2}+\beta _{6})q^{3}+(\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\) |