Defining parameters
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.c (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(6\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{13}(5, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 14 | 14 | 0 |
Cusp forms | 10 | 10 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{13}^{\mathrm{new}}(5, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
5.13.c.a | $10$ | $4.570$ | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) | None | \(-2\) | \(318\) | \(-4250\) | \(279598\) | \(q+\beta _{5}q^{2}+(31-31\beta _{1}-\beta _{3}+3\beta _{6}+\cdots)q^{3}+\cdots\) |