Space of modular forms of level 22, weight 7, and Character 22.b

• Label: 22.7.b
• Level: $22$
• Weight: $7$
• Character orbit: 22.b
• Rep. character: $\chi_{22}(21,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $21$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	22.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(21\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(22, [\chi])\).

	Total	New	Old
Modular forms	20	6	14
Cusp forms	16	6	10
Eisenstein series	4	0	4

Trace form

\( 6 q - 52 q^{3} - 192 q^{4} + 368 q^{5} - 346 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(22, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
22.7.b.a	$22$	$7$	22.b	11.b	$2$	$6$	$6$	$5.061$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(0\)	\(-52\)	\(368\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(-9+\beta _{1})q^{3}-2^{5}q^{4}+(61+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(22, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(22, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)