Defining parameters
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(22\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(6))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 23 | 3 | 20 |
Cusp forms | 19 | 3 | 16 |
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 |
---|---|---|---|
\(+\) | \(-\) | \(-\) | \(1\) |
\(-\) | \(+\) | \(-\) | \(1\) |
\(-\) | \(-\) | \(+\) | \(1\) |
Plus space | \(+\) | \(1\) | |
Minus space | \(-\) | \(2\) |
Trace form
Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(6))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | |||||||
6.22.a.a | $1$ | $16.769$ | \(\Q\) | None | \(-1024\) | \(59049\) | \(26444550\) | \(166115864\) | $+$ | $-$ | \(q-2^{10}q^{2}+3^{10}q^{3}+2^{20}q^{4}+26444550q^{5}+\cdots\) | |
6.22.a.b | $1$ | $16.769$ | \(\Q\) | None | \(1024\) | \(-59049\) | \(12954174\) | \(-479513104\) | $-$ | $+$ | \(q+2^{10}q^{2}-3^{10}q^{3}+2^{20}q^{4}+12954174q^{5}+\cdots\) | |
6.22.a.c | $1$ | $16.769$ | \(\Q\) | None | \(1024\) | \(59049\) | \(-23245050\) | \(-1322977768\) | $-$ | $-$ | \(q+2^{10}q^{2}+3^{10}q^{3}+2^{20}q^{4}-23245050q^{5}+\cdots\) |
Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(6))\) into lower level spaces
\( S_{22}^{\mathrm{old}}(\Gamma_0(6)) \simeq \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)