Defining parameters
Level: | \( N \) | \(=\) | \( 22 = 2 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 22.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(42\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(22))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 41 | 9 | 32 |
Cusp forms | 37 | 9 | 28 |
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 |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(2\) |
\(+\) | \(-\) | $-$ | \(2\) |
\(-\) | \(+\) | $-$ | \(3\) |
\(-\) | \(-\) | $+$ | \(2\) |
Plus space | \(+\) | \(4\) | |
Minus space | \(-\) | \(5\) |
Trace form
Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(22))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 11 | |||||||
22.14.a.a | $2$ | $23.591$ | \(\Q(\sqrt{100039}) \) | None | \(-128\) | \(-662\) | \(-48566\) | \(404508\) | $+$ | $+$ | \(q-2^{6}q^{2}+(-331+\beta )q^{3}+2^{12}q^{4}+\cdots\) | |
22.14.a.b | $2$ | $23.591$ | \(\Q(\sqrt{55441}) \) | None | \(-128\) | \(1626\) | \(7666\) | \(637048\) | $+$ | $-$ | \(q-2^{6}q^{2}+(813-3\beta )q^{3}+2^{12}q^{4}+\cdots\) | |
22.14.a.c | $2$ | $23.591$ | \(\Q(\sqrt{45769}) \) | None | \(128\) | \(-926\) | \(2914\) | \(-170560\) | $-$ | $-$ | \(q+2^{6}q^{2}+(-463-\beta )q^{3}+2^{12}q^{4}+\cdots\) | |
22.14.a.d | $3$ | $23.591$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(192\) | \(-298\) | \(40432\) | \(40452\) | $-$ | $+$ | \(q+2^{6}q^{2}+(-10^{2}-\beta _{1}-\beta _{2})q^{3}+2^{12}q^{4}+\cdots\) |
Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(22))\) into lower level spaces
\( S_{14}^{\mathrm{old}}(\Gamma_0(22)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)