Defining parameters
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(16\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_0(8))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 17 | 4 | 13 |
Cusp forms | 13 | 4 | 9 |
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 |
---|---|
\(+\) | \(2\) |
\(-\) | \(2\) |
Trace form
Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_0(8))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | |||||||
8.16.a.a | $1$ | $11.415$ | \(\Q\) | None | \(0\) | \(-3444\) | \(313358\) | \(-2324616\) | $-$ | \(q-3444q^{3}+313358q^{5}-2324616q^{7}+\cdots\) | |
8.16.a.b | $1$ | $11.415$ | \(\Q\) | None | \(0\) | \(2700\) | \(-251890\) | \(1374072\) | $-$ | \(q+2700q^{3}-251890q^{5}+1374072q^{7}+\cdots\) | |
8.16.a.c | $2$ | $11.415$ | \(\Q(\sqrt{58}) \) | None | \(0\) | \(-4072\) | \(-140260\) | \(126192\) | $+$ | \(q+(-2036+\beta )q^{3}+(-70130+6^{2}\beta )q^{5}+\cdots\) |
Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_0(8))\) into lower level spaces
\( S_{16}^{\mathrm{old}}(\Gamma_0(8)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)