Defining parameters
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.h (of order \(18\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 37 \) |
Character field: | \(\Q(\zeta_{18})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(6\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(37, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 30 | 30 | 0 |
Cusp forms | 18 | 18 | 0 |
Eisenstein series | 12 | 12 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(37, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
37.2.h.a | $18$ | $0.295$ | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) | None | \(-9\) | \(-9\) | \(-3\) | \(-3\) | \(q+(\beta _{4}-\beta _{11})q^{2}+(-1-\beta _{12}+\beta _{16}+\cdots)q^{3}+\cdots\) |