Space of modular forms of level 6, weight 5, and Character 6.b

• Label: 6.5.b
• Level: $6$
• Weight: $5$
• Character orbit: 6.b
• Rep. character: $\chi_{6}(5,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $5$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(5\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(6, [\chi])\).

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

Trace form

2 * q - 6 * q^3 - 16 * q^4 + 48 * q^6 + 52 * q^7 - 126 * q^9 - 96 * q^10 + 48 * q^12 + 100 * q^13 + 288 * q^15 + 128 * q^16 - 288 * q^18 - 716 * q^19 - 156 * q^21 + 672 * q^22 - 384 * q^24 + 674 * q^25 + 1242 * q^27 - 416 * q^28 + 288 * q^30 - 1484 * q^31 - 2016 * q^33 - 1152 * q^34 + 1008 * q^36 + 3748 * q^37 - 300 * q^39 + 768 * q^40 + 1248 * q^42 - 524 * q^43 - 1728 * q^45 - 2112 * q^46 - 384 * q^48 - 3450 * q^49 + 3456 * q^51 - 800 * q^52 - 2160 * q^54 + 4032 * q^55 + 2148 * q^57 + 8160 * q^58 - 2304 * q^60 - 2972 * q^61 - 3276 * q^63 - 1024 * q^64 - 2016 * q^66 - 8972 * q^67 + 6336 * q^69 - 2496 * q^70 + 2304 * q^72 + 580 * q^73 - 2022 * q^75 + 5728 * q^76 + 2400 * q^78 + 19636 * q^79 + 2754 * q^81 - 13632 * q^82 + 1248 * q^84 - 6912 * q^85 - 24480 * q^87 - 5376 * q^88 + 6048 * q^90 + 2600 * q^91 + 4452 * q^93 + 9600 * q^94 + 3072 * q^96 - 956 * q^97 + 12096 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(6, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
6.5.b.a	$6$	$5$	6.b	3.b	$2$	$2$	$2$	$0.620$	\(\Q(\sqrt{-2}) \)	None		✓	✓	✓	6.5.b.a	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(52\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+(-3-3\beta )q^{3}-8q^{4}+6\beta q^{5}+\cdots\)