Defining parameters
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(44\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(16))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 45 | 11 | 34 |
Cusp forms | 39 | 10 | 29 |
Eisenstein series | 6 | 1 | 5 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | Dim. |
---|---|
\(+\) | \(5\) |
\(-\) | \(5\) |
Trace form
Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(16))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | |||||||
16.22.a.a | $1$ | $44.716$ | \(\Q\) | None | \(0\) | \(-71604\) | \(-28693770\) | \(853202392\) | $-$ | \(q-71604q^{3}-28693770q^{5}+853202392q^{7}+\cdots\) | |
16.22.a.b | $1$ | $44.716$ | \(\Q\) | None | \(0\) | \(-59316\) | \(4975350\) | \(-1427425832\) | $-$ | \(q-59316q^{3}+4975350q^{5}-1427425832q^{7}+\cdots\) | |
16.22.a.c | $1$ | $44.716$ | \(\Q\) | None | \(0\) | \(128844\) | \(21640950\) | \(768078808\) | $-$ | \(q+128844q^{3}+21640950q^{5}+768078808q^{7}+\cdots\) | |
16.22.a.d | $2$ | $44.716$ | \(\Q(\sqrt{2161}) \) | None | \(0\) | \(-65640\) | \(13689324\) | \(260508080\) | $-$ | \(q+(-32820-\beta )q^{3}+(6844662+204\beta )q^{5}+\cdots\) | |
16.22.a.e | $2$ | $44.716$ | \(\Q(\sqrt{358549}) \) | None | \(0\) | \(105432\) | \(2108140\) | \(-444771792\) | $+$ | \(q+(52716-\beta )q^{3}+(1054070-20\beta )q^{5}+\cdots\) | |
16.22.a.f | $3$ | $44.716$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(0\) | \(-96764\) | \(-24111774\) | \(-295988280\) | $+$ | \(q+(-32255+\beta _{1})q^{3}+(-8037261+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces
\( S_{22}^{\mathrm{old}}(\Gamma_0(16)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)