Defining parameters
Level: | \( N \) | \(=\) | \( 81 = 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 81.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(198\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(81))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 195 | 86 | 109 |
Cusp forms | 183 | 82 | 101 |
Eisenstein series | 12 | 4 | 8 |
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 |
---|---|
\(+\) | \(40\) |
\(-\) | \(42\) |
Trace form
Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(81))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | |||||||
81.22.a.a | $10$ | $226.377$ | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) | None | \(-1311\) | \(0\) | \(19406040\) | \(-413122630\) | $+$ | \(q+(-131-\beta _{1})q^{2}+(1023916+187\beta _{1}+\cdots)q^{4}+\cdots\) | |
81.22.a.b | $10$ | $226.377$ | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) | None | \(1311\) | \(0\) | \(-19406040\) | \(-413122630\) | $+$ | \(q+(131+\beta _{1})q^{2}+(1023916+187\beta _{1}+\cdots)q^{4}+\cdots\) | |
81.22.a.c | $20$ | $226.377$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(-1023\) | \(0\) | \(-32234853\) | \(189623959\) | $+$ | \(q+(-51-\beta _{1})q^{2}+(996143+29\beta _{1}+\cdots)q^{4}+\cdots\) | |
81.22.a.d | $20$ | $226.377$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(1023\) | \(0\) | \(32234853\) | \(189623959\) | $-$ | \(q+(51+\beta _{1})q^{2}+(996143+29\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\) | |
81.22.a.e | $22$ | $226.377$ | None | \(0\) | \(0\) | \(0\) | \(67749428\) | $-$ |
Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(81))\) into lower level spaces
\( S_{22}^{\mathrm{old}}(\Gamma_0(81)) \simeq \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 2}\)