Defining parameters
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(10\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_0(4))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 11 | 1 | 10 |
Cusp forms | 8 | 1 | 7 |
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 \(S_{20}^{\mathrm{new}}(\Gamma_0(4))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | |||||||
4.20.a.a | $1$ | $9.153$ | \(\Q\) | None | \(0\) | \(-36\) | \(-196290\) | \(-35905576\) | $-$ | \(q-6^{2}q^{3}-196290q^{5}-35905576q^{7}+\cdots\) |
Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_0(4))\) into lower level spaces
\( S_{20}^{\mathrm{old}}(\Gamma_0(4)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)