Space of modular forms of level 12, weight 4, and Character 12.b

• Label: 12.4.b
• Level: $12$
• Weight: $4$
• Character orbit: 12.b
• Rep. character: $\chi_{12}(11,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(8\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(12, [\chi])\).

	Total	New	Old
Modular forms	8	8	0
Cusp forms	4	4	0
Eisenstein series	4	4	0

Trace form

4 * q - 8 * q^4 - 24 * q^6 - 12 * q^9 + 80 * q^10 + 120 * q^12 - 40 * q^13 - 224 * q^16 - 240 * q^18 + 120 * q^21 + 240 * q^22 + 288 * q^24 + 180 * q^25 - 240 * q^28 - 240 * q^30 - 480 * q^33 + 320 * q^34 + 24 * q^36 - 520 * q^37 + 320 * q^40 + 240 * q^42 + 960 * q^45 - 672 * q^46 - 480 * q^48 + 1132 * q^49 + 80 * q^52 + 792 * q^54 - 1080 * q^57 - 1360 * q^58 - 960 * q^60 - 1768 * q^61 + 1408 * q^64 + 1200 * q^66 + 1344 * q^69 + 480 * q^70 - 960 * q^72 + 1640 * q^73 + 2160 * q^76 + 240 * q^78 - 2844 * q^81 - 1120 * q^82 - 240 * q^84 - 1280 * q^85 - 2880 * q^88 - 240 * q^90 + 3480 * q^93 - 1344 * q^94 + 384 * q^96 + 3080 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(12, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
12.4.b.a	$12$	$4$	12.b	12.b	$2$	$4$	$4$	$0.708$	\(\Q(\sqrt{3}, \sqrt{-5})\)	None		✓	✓	✓	12.4.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)