Defining parameters
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(2\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(3))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3 | 1 | 2 |
Cusp forms | 1 | 1 | 0 |
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.
\(3\) | Dim |
---|---|
\(+\) | \(1\) |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(3))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | |||||||
3.8.a.a | $1$ | $0.937$ | \(\Q\) | None | \(6\) | \(-27\) | \(390\) | \(-64\) | $+$ | \(q+6q^{2}-3^{3}q^{3}-92q^{4}+390q^{5}+\cdots\) |