Defining parameters
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 37 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(19\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(37, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 18 | 18 | 0 |
Cusp forms | 16 | 16 | 0 |
Eisenstein series | 2 | 2 | 0 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(37, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
37.6.b.a | $16$ | $5.934$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(-18\) | \(0\) | \(190\) | \(q+\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(-17+\beta _{2}+\cdots)q^{4}+\cdots\) |