Defining parameters
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(1\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_0(1))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2 | 2 | 0 |
Cusp forms | 1 | 1 | 0 |
Eisenstein series | 1 | 1 | 0 |
Trace form
Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_0(1))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | Fricke sign | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | |||||||
1.20.a.a | $1$ | $2.288$ | \(\Q\) | None | \(456\) | \(50652\) | \(-2377410\) | \(-16917544\) | $+$ | \(q+456q^{2}+50652q^{3}-316352q^{4}+\cdots\) |