Defining parameters
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(6\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_0(2))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 7 | 3 | 4 |
Cusp forms | 5 | 3 | 2 |
Eisenstein series | 2 | 0 | 2 |
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 \(S_{26}^{\mathrm{new}}(\Gamma_0(2))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | |||||||
2.26.a.a | $1$ | $7.920$ | \(\Q\) | None | \(-4096\) | \(97956\) | \(341005350\) | \(-40882637368\) | $+$ | \(q-2^{12}q^{2}+97956q^{3}+2^{24}q^{4}+341005350q^{5}+\cdots\) | |
2.26.a.b | $2$ | $7.920$ | \(\Q(\sqrt{106705}) \) | None | \(8192\) | \(379848\) | \(741953100\) | \(-376536944\) | $-$ | \(q+2^{12}q^{2}+(189924-\beta )q^{3}+2^{24}q^{4}+\cdots\) |
Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces
\( S_{26}^{\mathrm{old}}(\Gamma_0(2)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)