Defining parameters
Level: | \( N \) | \(=\) | \( 6561 = 3^{8} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6561.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(1458\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6561))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 783 | 342 | 441 |
Cusp forms | 676 | 306 | 370 |
Eisenstein series | 107 | 36 | 71 |
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 |
---|---|
\(+\) | \(144\) |
\(-\) | \(162\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6561))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | |||||||
6561.2.a.a | $36$ | $52.390$ | None | \(-9\) | \(0\) | \(0\) | \(-18\) | $+$ | |||
6561.2.a.b | $36$ | $52.390$ | None | \(9\) | \(0\) | \(0\) | \(-18\) | $+$ | |||
6561.2.a.c | $72$ | $52.390$ | None | \(-9\) | \(0\) | \(-18\) | \(0\) | $+$ | |||
6561.2.a.d | $72$ | $52.390$ | None | \(9\) | \(0\) | \(18\) | \(0\) | $-$ | |||
6561.2.a.e | $90$ | $52.390$ | None | \(0\) | \(0\) | \(0\) | \(36\) | $-$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6561))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6561)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(243))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(729))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2187))\)\(^{\oplus 2}\)