Space of modular forms of level 2, weight 22, and trivial character

• Label: 2.22.a
• Level: $2$
• Weight: $22$
• Character orbit: 2.a
• Rep. character: $\chi_{2}(1,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $5$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(5\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(2))\).

	Total	New	Old
Modular forms	6	2	4
Cusp forms	4	2	2
Eisenstein series	2	0	2

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.
\(+\)	\(1\)
\(-\)	\(1\)

Trace form

\( 2 q + 130920 q^{3} + 2097152 q^{4} - 23718420 q^{5} - 12582912 q^{6} + 574223440 q^{7} - 12275185734 q^{9} + O(q^{10}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(2))\) 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
2.22.a.a	$2$	$22$	2.a	1.a	$1$	$1$	$1$	$5.590$	\(\Q\)	None	✓	$1$	$1$	\(-1024\)	\(71604\)	\(-28693770\)	\(-853202392\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{10}q^{2}+71604q^{3}+2^{20}q^{4}-28693770q^{5}+\cdots\)
2.22.a.b	$2$	$22$	2.a	1.a	$1$	$1$	$1$	$5.590$	\(\Q\)	None	✓	$1$	$0$	\(1024\)	\(59316\)	\(4975350\)	\(1427425832\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{10}q^{2}+59316q^{3}+2^{20}q^{4}+4975350q^{5}+\cdots\)

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_0(2)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)