Defining parameters
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.k (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(336\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(882, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 400 | 24 | 376 |
Cusp forms | 272 | 24 | 248 |
Eisenstein series | 128 | 0 | 128 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(882, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
882.2.k.a | $8$ | $7.043$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+(\zeta_{24}-2\zeta_{24}^{3}+\cdots)q^{5}+\cdots\) |
882.2.k.b | $16$ | $7.043$ | \(\Q(\zeta_{48})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{48}+\zeta_{48}^{5})q^{2}+(1-\zeta_{48}^{3})q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(882, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)