Defining parameters
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(22\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(8))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 23 | 5 | 18 |
Cusp forms | 19 | 5 | 14 |
Eisenstein series | 4 | 0 | 4 |
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 |
---|---|
\(+\) | \(2\) |
\(-\) | \(3\) |
Trace form
Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(8))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | |||||||
8.22.a.a | $2$ | $22.358$ | \(\Q(\sqrt{358549}) \) | None | \(0\) | \(-105432\) | \(2108140\) | \(444771792\) | $+$ | \(q+(-52716-\beta )q^{3}+(1054070+20\beta )q^{5}+\cdots\) | |
8.22.a.b | $3$ | $22.358$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(0\) | \(96764\) | \(-24111774\) | \(295988280\) | $-$ | \(q+(32255-\beta _{1})q^{3}+(-8037261+9\beta _{1}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(8))\) into lower level spaces
\( S_{22}^{\mathrm{old}}(\Gamma_0(8)) \simeq \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)