Space of modular forms of level 223, weight 2, and Character 223.c

• Label: 223.2.c
• Level: $223$
• Weight: $2$
• Character orbit: 223.c
• Rep. character: $\chi_{223}(39,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $36$
• Newform subspaces: $1$
• Sturm bound: $37$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	223.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 223 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(37\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(223, [\chi])\).

	Total	New	Old
Modular forms	40	40	0
Cusp forms	36	36	0
Eisenstein series	4	4	0

Trace form

36 * q - 4 * q^2 - q^3 + 32 * q^4 + 3 * q^5 + 9 * q^6 - 2 * q^7 - 6 * q^8 - 11 * q^9 - 3 * q^10 - q^11 - 11 * q^12 - 26 * q^13 + 6 * q^15 + 24 * q^16 + 8 * q^17 + 14 * q^18 - 4 * q^19 - 5 * q^20 - 3 * q^21 - 2 * q^22 + 8 * q^23 - q^24 - 13 * q^25 - 22 * q^26 - 16 * q^27 - 74 * q^28 + 10 * q^29 + 14 * q^30 + 16 * q^31 + 4 * q^32 + 18 * q^33 - 20 * q^34 - 5 * q^35 + 27 * q^36 + 10 * q^37 + q^38 + q^39 - 27 * q^40 - 20 * q^41 + 5 * q^42 + 14 * q^43 - 37 * q^44 + 21 * q^45 - 30 * q^46 - 37 * q^48 + 90 * q^49 + 50 * q^50 - 26 * q^51 - 98 * q^52 + 2 * q^53 - 52 * q^54 + q^55 - 110 * q^56 + 25 * q^57 - 5 * q^58 - 16 * q^59 + 28 * q^60 - 21 * q^61 - 24 * q^62 - 20 * q^63 + 50 * q^64 + 60 * q^66 - 3 * q^67 + 82 * q^68 + 3 * q^69 + 3 * q^70 + 25 * q^71 + 25 * q^72 - 3 * q^73 + 19 * q^74 + 3 * q^75 + q^76 - q^77 - 13 * q^78 - 13 * q^79 - 32 * q^80 + 18 * q^81 - 40 * q^82 - 4 * q^83 - 33 * q^84 - 6 * q^85 - 3 * q^86 + 40 * q^87 + 35 * q^88 - 11 * q^89 + 12 * q^90 + 4 * q^91 + 25 * q^92 - 5 * q^93 + 3 * q^94 - 100 * q^95 + 6 * q^96 - 28 * q^97 + 18 * q^98 - 15 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(223, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
223.2.c.a	$223$	$2$	223.c	223.c	$3$	$36$	$18$	$1.781$		None		✓	✓	✓	223.2.c.a	$2$	$0$	\(-4\)	\(-1\)	\(3\)	\(-2\)		$\mathrm{SU}(2)[C_{3}]$