Defining parameters
Level: | \( N \) | \(=\) | \( 538 = 2 \cdot 269 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 538.e (of order \(134\) and degree \(66\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 269 \) |
Character field: | \(\Q(\zeta_{134})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(135\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(538, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 4620 | 1452 | 3168 |
Cusp forms | 4356 | 1452 | 2904 |
Eisenstein series | 264 | 0 | 264 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(538, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
538.2.e.a | $1452$ | $4.296$ | None | \(0\) | \(0\) | \(-2\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(538, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(538, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(269, [\chi])\)\(^{\oplus 2}\)