Space of modular forms of level 22, weight 2, and Character 22.c

• Label: 22.2.c
• Level: $22$
• Weight: $2$
• Character orbit: 22.c
• Rep. character: $\chi_{22}(3,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	22.c (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(6\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(22, [\chi])\).

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

Trace form

\( 4 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} + q^{6} + 2 q^{7} - q^{8} + 7 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(22, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
22.2.c.a	$22$	$2$	22.c	11.c	$5$	$4$	$1$	$0.176$	\(\Q(\zeta_{10})\)	None		$2$	$0$	\(-1\)	\(-4\)	\(-6\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots\)