Defining parameters
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(14\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(8))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 15 | 3 | 12 |
Cusp forms | 11 | 3 | 8 |
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 |
---|---|
\(+\) | \(1\) |
\(-\) | \(2\) |
Trace form
Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(8))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | |||||||
8.14.a.a | $1$ | $8.578$ | \(\Q\) | None | \(0\) | \(-12\) | \(-4330\) | \(-139992\) | $+$ | \(q-12q^{3}-4330q^{5}-139992q^{7}+\cdots\) | |
8.14.a.b | $2$ | $8.578$ | \(\Q(\sqrt{781}) \) | None | \(0\) | \(872\) | \(18476\) | \(110928\) | $-$ | \(q+(436-\beta )q^{3}+(9238-12\beta )q^{5}+(55464+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(8))\) into lower level spaces
\( S_{14}^{\mathrm{old}}(\Gamma_0(8)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)