Defining parameters
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(8\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(9))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 9 | 4 | 5 |
Cusp forms | 5 | 3 | 2 |
Eisenstein series | 4 | 1 | 3 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | Dim |
---|---|
\(+\) | \(2\) |
\(-\) | \(1\) |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(9))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | |||||||
9.8.a.a | $1$ | $2.811$ | \(\Q\) | None | \(-6\) | \(0\) | \(-390\) | \(-64\) | $-$ | \(q-6q^{2}-92q^{4}-390q^{5}-2^{6}q^{7}+\cdots\) | |
9.8.a.b | $2$ | $2.811$ | \(\Q(\sqrt{10}) \) | None | \(0\) | \(0\) | \(0\) | \(520\) | $+$ | \(q+\beta q^{2}+232q^{4}-2^{4}\beta q^{5}+260q^{7}+\cdots\) |
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(9))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_0(9)) \simeq \) \(S_{8}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)