Defining parameters
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(12\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(10))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 13 | 1 | 12 |
Cusp forms | 9 | 1 | 8 |
Eisenstein series | 4 | 0 | 4 |
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 |
---|---|---|---|
\(-\) | \(-\) | $+$ | \(1\) |
Plus space | \(+\) | \(1\) | |
Minus space | \(-\) | \(0\) |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(10))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 5 | |||||||
10.8.a.a | $1$ | $3.124$ | \(\Q\) | None | \(8\) | \(28\) | \(125\) | \(104\) | $-$ | $-$ | \(q+8q^{2}+28q^{3}+2^{6}q^{4}+5^{3}q^{5}+224q^{6}+\cdots\) |
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(10))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_0(10)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)