Defining parameters
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.m (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(84, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 268 | 22 | 246 |
Cusp forms | 244 | 22 | 222 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(84, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
84.9.m.a | $10$ | $34.220$ | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) | None | \(0\) | \(-405\) | \(1389\) | \(1217\) | \(q+(-54+3^{3}\beta _{1})q^{3}+(92+93\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots\) |
84.9.m.b | $12$ | $34.220$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(486\) | \(285\) | \(198\) | \(q+(54-3^{3}\beta _{1})q^{3}+(2^{4}+2^{4}\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{9}^{\mathrm{old}}(84, [\chi])\) into lower level spaces
\( S_{9}^{\mathrm{old}}(84, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)