Defining parameters
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.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 \(M_{10}(\Gamma_0(6))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 11 | 1 | 10 |
Cusp forms | 7 | 1 | 6 |
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.
\(2\) | \(3\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(-\) | $-$ | \(1\) |
Plus space | \(+\) | \(0\) | |
Minus space | \(-\) | \(1\) |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(6))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | |||||||
6.10.a.a | $1$ | $3.090$ | \(\Q\) | None | \(-16\) | \(81\) | \(2694\) | \(-3544\) | $+$ | $-$ | \(q-2^{4}q^{2}+3^{4}q^{3}+2^{8}q^{4}+2694q^{5}+\cdots\) |
Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(6))\) into lower level spaces
\( S_{10}^{\mathrm{old}}(\Gamma_0(6)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)