Defining parameters
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(11\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(4))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 12 | 2 | 10 |
Cusp forms | 9 | 2 | 7 |
Eisenstein series | 3 | 0 | 3 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | Dim. |
---|---|
\(-\) | \(2\) |
Trace form
Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(4))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | |||||||
4.22.a.a | $2$ | $11.179$ | \(\Q(\sqrt{2161}) \) | None | \(0\) | \(65640\) | \(13689324\) | \(-260508080\) | $-$ | \(q+(32820-\beta )q^{3}+(6844662-204\beta )q^{5}+\cdots\) |
Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(4))\) into lower level spaces
\( S_{22}^{\mathrm{old}}(\Gamma_0(4)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)