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 + 4 * q^10 - q^11 + 6 * q^12 - 4 * q^13 + 2 * q^14 + 6 * q^15 - q^16 + 2 * q^17 - 8 * q^18 - 5 * q^19 - 6 * q^20 - 12 * q^21 - 11 * q^22 - 4 * q^23 + q^24 + 9 * q^25 + 6 * q^26 + 5 * q^27 + 2 * q^28 + 10 * q^29 + 6 * q^30 - 2 * q^31 + 4 * q^32 + 11 * q^33 + 2 * q^34 + 12 * q^35 - 8 * q^36 - 18 * q^37 + 10 * q^38 - 6 * q^39 + 4 * q^40 - 2 * q^41 - 2 * q^42 + 6 * q^43 + 4 * q^44 - 28 * q^45 - 4 * q^46 - 8 * q^47 - 4 * q^48 + 3 * q^49 - 11 * q^50 - 7 * q^51 + 6 * q^52 - 4 * q^53 + 4 * q^55 - 8 * q^56 + 5 * q^57 + 10 * q^58 + 5 * q^59 - 4 * q^60 + 8 * q^61 - 2 * q^62 + 16 * q^63 - q^64 + 16 * q^65 + 16 * q^66 + 22 * q^67 + 2 * q^68 + 14 * q^69 - 8 * q^70 + 8 * q^71 + 7 * q^72 - 14 * q^73 - 18 * q^74 - 9 * q^75 - 10 * q^76 - 8 * q^77 - 16 * q^78 - 30 * q^79 + 4 * q^80 + 14 * q^81 - 7 * q^82 - 19 * q^83 + 8 * q^84 + 2 * q^85 + 21 * q^86 - 20 * q^87 - q^88 - 10 * q^89 + 12 * q^90 - 12 * q^91 + 6 * q^92 + 2 * q^93 + 12 * q^94 - 10 * q^95 - 4 * q^96 - 3 * q^97 - 12 * q^98 - 13 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	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		✓	✓	✓	22.2.c.a	$2$	$0$	\(-1\)	\(-4\)	\(-6\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots\)