Defining parameters
Level: | \( N \) | \(=\) | \( 22 = 2 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 22.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(12\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(22))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 11 | 3 | 8 |
Cusp forms | 7 | 3 | 4 |
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.
\(2\) | \(11\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(1\) |
\(+\) | \(-\) | $-$ | \(1\) |
\(-\) | \(-\) | $+$ | \(1\) |
Plus space | \(+\) | \(2\) | |
Minus space | \(-\) | \(1\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(22))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 11 | |||||||
22.4.a.a | $1$ | $1.298$ | \(\Q\) | None | \(-2\) | \(-7\) | \(-19\) | \(14\) | $+$ | $-$ | \(q-2q^{2}-7q^{3}+4q^{4}-19q^{5}+14q^{6}+\cdots\) | |
22.4.a.b | $1$ | $1.298$ | \(\Q\) | None | \(-2\) | \(4\) | \(14\) | \(-8\) | $+$ | $+$ | \(q-2q^{2}+4q^{3}+4q^{4}+14q^{5}-8q^{6}+\cdots\) | |
22.4.a.c | $1$ | $1.298$ | \(\Q\) | None | \(2\) | \(1\) | \(-3\) | \(-10\) | $-$ | $-$ | \(q+2q^{2}+q^{3}+4q^{4}-3q^{5}+2q^{6}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(22))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(22)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)