Space of modular forms of level 16, weight 22, and trivial character

• Label: 16.22.a
• Level: $16$
• Weight: $22$
• Character orbit: 16.a
• Rep. character: $\chi_{16}(1,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $6$
• Sturm bound: $44$
• Trace bound: $3$

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

\( 10 q - 59048 q^{3} - 10391780 q^{5} - 286396624 q^{7} + 36243817378 q^{9} + O(q^{10}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(16))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2
16.22.a.a	$16$	$22$	16.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-71604\)	\(-28693770\)	\(853202392\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-71604q^{3}-28693770q^{5}+853202392q^{7}+\cdots\)
16.22.a.b	$16$	$22$	16.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-59316\)	\(4975350\)	\(-1427425832\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-59316q^{3}+4975350q^{5}-1427425832q^{7}+\cdots\)
16.22.a.c	$16$	$22$	16.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(128844\)	\(21640950\)	\(768078808\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+128844q^{3}+21640950q^{5}+768078808q^{7}+\cdots\)
16.22.a.d	$16$	$22$	16.a	1.a	$1$	$2$	$2$	$44.716$	\(\Q(\sqrt{2161}) \)	None	✓	$1$	$0$	\(0\)	\(-65640\)	\(13689324\)	\(260508080\)		$-$	$-$	$2^{8}\cdot 3\cdot 7$	$\mathrm{SU}(2)$	\(q+(-32820-\beta )q^{3}+(6844662+204\beta )q^{5}+\cdots\)
16.22.a.e	$16$	$22$	16.a	1.a	$1$	$2$	$2$	$44.716$	\(\Q(\sqrt{358549}) \)	None	✓	$1$	$1$	\(0\)	\(105432\)	\(2108140\)	\(-444771792\)		$+$	$+$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+(52716-\beta )q^{3}+(1054070-20\beta )q^{5}+\cdots\)
16.22.a.f	$16$	$22$	16.a	1.a	$1$	$3$	$3$	$44.716$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-96764\)	\(-24111774\)	\(-295988280\)		$+$	$+$	$2^{21}\cdot 3\cdot 5\cdot 7$	$\mathrm{SU}(2)$	\(q+(-32255+\beta _{1})q^{3}+(-8037261+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_0(16)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)