Defining parameters
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(8\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(8))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 9 | 2 | 7 |
Cusp forms | 5 | 2 | 3 |
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 |
---|---|
\(+\) | \(1\) |
\(-\) | \(1\) |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(8))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | |||||||
8.8.a.a | $1$ | $2.499$ | \(\Q\) | None | \(0\) | \(-84\) | \(-82\) | \(-456\) | $-$ | \(q-84q^{3}-82q^{5}-456q^{7}+4869q^{9}+\cdots\) | |
8.8.a.b | $1$ | $2.499$ | \(\Q\) | None | \(0\) | \(44\) | \(430\) | \(-1224\) | $+$ | \(q+44q^{3}+430q^{5}-1224q^{7}-251q^{9}+\cdots\) |
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(8))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_0(8)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)