Defining parameters
Level: | \( N \) | \(=\) | \( 209 = 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 209.j (of order \(9\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 19 \) |
Character field: | \(\Q(\zeta_{9})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(40\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(209, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 132 | 96 | 36 |
Cusp forms | 108 | 96 | 12 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(209, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
209.2.j.a | $6$ | $1.669$ | \(\Q(\zeta_{18})\) | None | \(3\) | \(0\) | \(6\) | \(6\) | \(q+(1-\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{2}+\cdots\) |
209.2.j.b | $42$ | $1.669$ | None | \(-3\) | \(0\) | \(-6\) | \(-6\) | ||
209.2.j.c | $48$ | $1.669$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(209, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(209, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)