Defining parameters
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 24 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_0(9))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 25 | 10 | 15 |
Cusp forms | 21 | 9 | 12 |
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 |
---|---|
\(+\) | \(4\) |
\(-\) | \(5\) |
Trace form
Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(9))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | |||||||
9.24.a.a | $1$ | $30.168$ | \(\Q\) | None | \(-1128\) | \(0\) | \(48863730\) | \(-1723688680\) | $-$ | \(q-1128q^{2}-7116224q^{4}+48863730q^{5}+\cdots\) | |
9.24.a.b | $2$ | $30.168$ | \(\Q(\sqrt{144169}) \) | None | \(-1080\) | \(0\) | \(-73069020\) | \(-1359184400\) | $-$ | \(q+(-540-\beta )q^{2}+(12663328+1080\beta )q^{4}+\cdots\) | |
9.24.a.c | $2$ | $30.168$ | \(\Q(\sqrt{530401}) \) | None | \(1242\) | \(0\) | \(46808820\) | \(-211963904\) | $-$ | \(q+(621-\beta )q^{2}+(-3229358-1242\beta )q^{4}+\cdots\) | |
9.24.a.d | $4$ | $30.168$ | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(8561438480\) | $+$ | \(q+\beta _{1}q^{2}+(4777492+\beta _{3})q^{4}+(17070\beta _{1}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_0(9))\) into lower level spaces
\( S_{24}^{\mathrm{old}}(\Gamma_0(9)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)