Defining parameters
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
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 \(M_{6}(\Gamma_0(3))\).
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 \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\) into newform subspaces
Label | Dim. | \(A\) | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | 3 | |||||||
3.6.a.a | \(1\) | \(0.481\) | \(\Q\) | None | \(-6\) | \(9\) | \(6\) | \(-40\) | \(-\) | \(q-6q^{2}+9q^{3}+4q^{4}+6q^{5}-54q^{6}+\cdots\) |