Defining parameters
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(26\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_0(9))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 27 | 11 | 16 |
Cusp forms | 23 | 10 | 13 |
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 |
---|---|
\(+\) | \(4\) |
\(-\) | \(6\) |
Trace form
Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_0(9))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | |||||||
9.26.a.a | $1$ | $35.640$ | \(\Q\) | None | \(48\) | \(0\) | \(741989850\) | \(39080597192\) | $-$ | \(q+48q^{2}-33552128q^{4}+741989850q^{5}+\cdots\) | |
9.26.a.b | $2$ | $35.640$ | \(\Q(\sqrt{1287001}) \) | None | \(324\) | \(0\) | \(-570861756\) | \(-29687385728\) | $-$ | \(q+(162-\beta )q^{2}+(12803848-18^{2}\beta )q^{4}+\cdots\) | |
9.26.a.c | $3$ | $35.640$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(3678\) | \(0\) | \(163152750\) | \(-9622572744\) | $-$ | \(q+(1226-\beta _{1})q^{2}+(30249196-1499\beta _{1}+\cdots)q^{4}+\cdots\) | |
9.26.a.d | $4$ | $35.640$ | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-40689469840\) | $+$ | \(q+\beta _{1}q^{2}+(34366048+\beta _{3})q^{4}+(-64017\beta _{1}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_0(9))\) into lower level spaces
\( S_{26}^{\mathrm{old}}(\Gamma_0(9)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)