Defining parameters
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.cw (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 273 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(224\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(819, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 240 | 76 | 164 |
Cusp forms | 208 | 76 | 132 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(819, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
819.2.cw.a | $8$ | $6.540$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(20\) | \(q+(\zeta_{24}-\zeta_{24}^{5}+\zeta_{24}^{7})q^{2}+(-\zeta_{24}^{2}+\cdots)q^{4}+\cdots\) |
819.2.cw.b | $68$ | $6.540$ | None | \(0\) | \(0\) | \(0\) | \(-14\) |
Decomposition of \(S_{2}^{\mathrm{old}}(819, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(819, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)