Defining parameters
Level: | \( N \) | \(=\) | \( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 714.bk (of order \(48\) and degree \(16\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 357 \) |
Character field: | \(\Q(\zeta_{48})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(714, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2432 | 768 | 1664 |
Cusp forms | 2176 | 768 | 1408 |
Eisenstein series | 256 | 0 | 256 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(714, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
714.2.bk.a | $384$ | $5.701$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
714.2.bk.b | $384$ | $5.701$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(714, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(714, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 2}\)