Defining parameters
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(7\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(3))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 8 | 4 | 4 |
Cusp forms | 6 | 4 | 2 |
Eisenstein series | 2 | 0 | 2 |
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 |
---|---|
\(+\) | \(2\) |
\(-\) | \(2\) |
Trace form
Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(3))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | |||||||
3.22.a.a | $1$ | $8.384$ | \(\Q\) | None | \(-2844\) | \(-59049\) | \(3109950\) | \(363303920\) | $+$ | \(q-2844q^{2}-3^{10}q^{3}+5991184q^{4}+\cdots\) | |
3.22.a.b | $1$ | $8.384$ | \(\Q\) | None | \(1728\) | \(-59049\) | \(-41512770\) | \(538429808\) | $+$ | \(q+12^{3}q^{2}-3^{10}q^{3}+888832q^{4}+\cdots\) | |
3.22.a.c | $2$ | $8.384$ | \(\Q(\sqrt{649}) \) | None | \(666\) | \(118098\) | \(996876\) | \(679896112\) | $-$ | \(q+(333-\beta )q^{2}+3^{10}q^{3}+(589618+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(3))\) into lower level spaces
\( S_{22}^{\mathrm{old}}(\Gamma_0(3)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)