Defining parameters
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 36 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(36\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{36}(\Gamma_0(9))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 37 | 15 | 22 |
Cusp forms | 33 | 14 | 19 |
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 |
---|---|
\(+\) | \(6\) |
\(-\) | \(8\) |
Trace form
Decomposition of \(S_{36}^{\mathrm{new}}(\Gamma_0(9))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | |||||||
9.36.a.a | $2$ | $69.836$ | \(\Q(\sqrt{2196841}) \) | None | \(60912\) | \(0\) | \(13\!\cdots\!40\) | \(-12\!\cdots\!44\) | $-$ | \(q+(30456-\beta )q^{2}+(28571469952+\cdots)q^{4}+\cdots\) | |
9.36.a.b | $3$ | $69.836$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(-139656\) | \(0\) | \(-892652054010\) | \(87\!\cdots\!56\) | $-$ | \(q+(-46552-\beta _{1})q^{2}+(11613754048+\cdots)q^{4}+\cdots\) | |
9.36.a.c | $3$ | $69.836$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(87330\) | \(0\) | \(-27\!\cdots\!10\) | \(48\!\cdots\!64\) | $-$ | \(q+(29110-\beta _{1})q^{2}+(10829584300+\cdots)q^{4}+\cdots\) | |
9.36.a.d | $6$ | $69.836$ | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-49\!\cdots\!00\) | $+$ | \(q+\beta _{1}q^{2}+(20719302952+\beta _{3})q^{4}+\cdots\) |
Decomposition of \(S_{36}^{\mathrm{old}}(\Gamma_0(9))\) into lower level spaces
\( S_{36}^{\mathrm{old}}(\Gamma_0(9)) \cong \) \(S_{36}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{36}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)