Defining parameters
Level: | \( N \) | \(=\) | \( 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 109.e (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 109 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(18\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(109, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20 | 20 | 0 |
Cusp forms | 16 | 16 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(109, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
109.2.e.a | $2$ | $0.870$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(1\) | \(-3\) | \(1\) | \(q+(-1+2\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-q^{4}+\cdots\) |
109.2.e.b | $14$ | $0.870$ | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) | None | \(0\) | \(-4\) | \(-2\) | \(-7\) | \(q-\beta _{1}q^{2}+(\beta _{5}+\beta _{10}-\beta _{13})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\) |