Defining parameters
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.i (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 39 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(28\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(117, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 36 | 12 | 24 |
Cusp forms | 20 | 12 | 8 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(117, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
117.2.i.a | $12$ | $0.934$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-8\) | \(q-\beta _{9}q^{2}+(\beta _{3}-2\beta _{4})q^{4}-\beta _{8}q^{5}+(-1+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(117, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(117, [\chi]) \cong \)