Defining parameters
Level: | \( N \) | \(=\) | \( 81 = 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 81.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(18\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(81))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 15 | 6 | 9 |
Cusp forms | 4 | 2 | 2 |
Eisenstein series | 11 | 4 | 7 |
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 |
---|---|
\(-\) | \(2\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(81))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | |||||||
81.2.a.a | $2$ | $0.647$ | \(\Q(\sqrt{3}) \) | None | \(0\) | \(0\) | \(0\) | \(4\) | $-$ | \(q+\beta q^{2}+q^{4}-\beta q^{5}+2q^{7}-\beta q^{8}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(81))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(81)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 2}\)