Defining parameters
Level: | \( N \) | \(=\) | \( 22 = 2 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 22.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(60\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_0(22))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 59 | 15 | 44 |
Cusp forms | 55 | 15 | 40 |
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 |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(4\) |
\(+\) | \(-\) | $-$ | \(4\) |
\(-\) | \(+\) | $-$ | \(3\) |
\(-\) | \(-\) | $+$ | \(4\) |
Plus space | \(+\) | \(8\) | |
Minus space | \(-\) | \(7\) |
Trace form
Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_0(22))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 11 | |||||||
22.20.a.a | $1$ | $50.340$ | \(\Q\) | None | \(512\) | \(-54309\) | \(7241785\) | \(-192705562\) | $-$ | $+$ | \(q+2^{9}q^{2}-54309q^{3}+2^{18}q^{4}+7241785q^{5}+\cdots\) | |
22.20.a.b | $2$ | $50.340$ | \(\Q(\sqrt{51151}) \) | None | \(1024\) | \(16974\) | \(-2948510\) | \(84929956\) | $-$ | $+$ | \(q+2^{9}q^{2}+(8487+9\beta )q^{3}+2^{18}q^{4}+\cdots\) | |
22.20.a.c | $4$ | $50.340$ | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) | None | \(-2048\) | \(7885\) | \(4557609\) | \(-208197214\) | $+$ | $+$ | \(q-2^{9}q^{2}+(1971-\beta _{1})q^{3}+2^{18}q^{4}+\cdots\) | |
22.20.a.d | $4$ | $50.340$ | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) | None | \(-2048\) | \(33119\) | \(-9916059\) | \(-61113046\) | $+$ | $-$ | \(q-2^{9}q^{2}+(8280-\beta _{1})q^{3}+2^{18}q^{4}+\cdots\) | |
22.20.a.e | $4$ | $50.340$ | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) | None | \(2048\) | \(66631\) | \(1538357\) | \(104176242\) | $-$ | $-$ | \(q+2^{9}q^{2}+(16658-\beta _{1})q^{3}+2^{18}q^{4}+\cdots\) |
Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_0(22))\) into lower level spaces
\( S_{20}^{\mathrm{old}}(\Gamma_0(22)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)