Defining parameters
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(20))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 24 | 3 | 21 |
Cusp forms | 18 | 3 | 15 |
Eisenstein series | 6 | 0 | 6 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(5\) | Fricke | Dim |
---|---|---|---|
\(-\) | \(+\) | $-$ | \(1\) |
\(-\) | \(-\) | $+$ | \(2\) |
Plus space | \(+\) | \(2\) | |
Minus space | \(-\) | \(1\) |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(20))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 5 | |||||||
20.8.a.a | $1$ | $6.248$ | \(\Q\) | None | \(0\) | \(-6\) | \(-125\) | \(-706\) | $-$ | $+$ | \(q-6q^{3}-5^{3}q^{5}-706q^{7}-2151q^{9}+\cdots\) | |
20.8.a.b | $2$ | $6.248$ | \(\Q(\sqrt{1129}) \) | None | \(0\) | \(-20\) | \(250\) | \(1660\) | $-$ | $-$ | \(q+(-10-\beta )q^{3}+5^{3}q^{5}+(830+9\beta )q^{7}+\cdots\) |
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(20))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_0(20)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 2}\)