Defining parameters
Level: | \( N \) | \(=\) | \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 798.p (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 399 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(320\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(5\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(798, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 336 | 104 | 232 |
Cusp forms | 304 | 104 | 200 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(798, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
798.2.p.a | $2$ | $6.372$ | \(\Q(\sqrt{-3}) \) | None | \(-2\) | \(3\) | \(0\) | \(4\) | \(q-q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(-1-\zeta_{6})q^{6}+\cdots\) |
798.2.p.b | $2$ | $6.372$ | \(\Q(\sqrt{-3}) \) | None | \(2\) | \(0\) | \(0\) | \(4\) | \(q+q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+(1-2\zeta_{6})q^{6}+\cdots\) |
798.2.p.c | $50$ | $6.372$ | None | \(-50\) | \(-3\) | \(0\) | \(0\) | ||
798.2.p.d | $50$ | $6.372$ | None | \(50\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(798, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(798, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 2}\)