Defining parameters
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(3\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(4))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 4 | 1 | 3 |
Cusp forms | 1 | 1 | 0 |
Eisenstein series | 3 | 0 | 3 |
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 |
---|---|
\(-\) | \(1\) |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | |||||||
4.6.a.a | $1$ | $0.642$ | \(\Q\) | None | \(0\) | \(-12\) | \(54\) | \(-88\) | $-$ | \(q-12q^{3}+54q^{5}-88q^{7}-99q^{9}+\cdots\) |