Space of modular forms of level 12, weight 3, and Character 12.d

• Label: 12.3.d
• Level: $12$
• Weight: $3$
• Character orbit: 12.d
• Rep. character: $\chi_{12}(7,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	12.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(6\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(12, [\chi])\).

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

Trace form

2 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 6 * q^6 + 16 * q^8 - 6 * q^9 + 4 * q^10 - 12 * q^12 + 4 * q^13 - 24 * q^14 - 16 * q^16 + 20 * q^17 + 6 * q^18 + 8 * q^20 + 24 * q^21 + 24 * q^22 - 42 * q^25 - 4 * q^26 + 48 * q^28 - 52 * q^29 - 12 * q^30 - 32 * q^32 - 24 * q^33 - 20 * q^34 + 12 * q^36 + 52 * q^37 + 72 * q^38 - 32 * q^40 + 116 * q^41 - 24 * q^42 - 48 * q^44 + 12 * q^45 - 96 * q^46 + 48 * q^48 + 2 * q^49 + 42 * q^50 - 8 * q^52 - 148 * q^53 - 18 * q^54 - 72 * q^57 + 52 * q^58 + 24 * q^60 + 52 * q^61 + 24 * q^62 + 128 * q^64 - 8 * q^65 + 24 * q^66 - 40 * q^68 + 96 * q^69 + 48 * q^70 - 48 * q^72 - 92 * q^73 - 52 * q^74 - 144 * q^76 + 96 * q^77 + 12 * q^78 + 32 * q^80 + 18 * q^81 - 116 * q^82 - 48 * q^84 - 40 * q^85 - 168 * q^86 + 164 * q^89 - 12 * q^90 + 192 * q^92 - 24 * q^93 + 240 * q^94 - 96 * q^96 + 4 * q^97 - 2 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(12, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
12.3.d.a	$12$	$3$	12.d	4.b	$2$	$2$	$2$	$0.327$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	12.3.d.a	$2$	$0$	\(-2\)	\(0\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta-1)q^{2}+\beta q^{3}+(2\beta-2)q^{4}+\cdots\)