Space of modular forms of level 28, weight 2, and Character 28.f

• Label: 28.2.f
• Level: $28$
• Weight: $2$
• Character orbit: 28.f
• Rep. character: $\chi_{28}(3,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	28.f (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(8\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(28, [\chi])\).

	Total	New	Old
Modular forms	12	12	0
Cusp forms	4	4	0
Eisenstein series	8	8	0

Trace form

4 * q - 2 * q^2 - 6 * q^5 - 8 * q^8 + 6 * q^10 + 12 * q^12 + 2 * q^14 + 8 * q^16 - 6 * q^17 + 6 * q^21 - 4 * q^22 - 12 * q^24 - 4 * q^25 - 12 * q^26 - 20 * q^28 + 16 * q^29 - 6 * q^30 + 8 * q^32 + 6 * q^33 - 6 * q^37 + 18 * q^38 + 12 * q^40 + 12 * q^42 + 4 * q^44 - 2 * q^46 - 4 * q^49 + 8 * q^50 + 2 * q^53 - 18 * q^54 + 16 * q^56 - 36 * q^57 - 8 * q^58 - 12 * q^60 - 18 * q^61 + 12 * q^65 - 6 * q^66 + 6 * q^70 + 30 * q^73 - 6 * q^74 - 10 * q^77 + 24 * q^78 - 24 * q^80 + 18 * q^81 + 12 * q^82 + 12 * q^85 - 4 * q^86 + 4 * q^88 + 54 * q^89 + 8 * q^92 + 6 * q^93 - 30 * q^94 - 24 * q^96 - 22 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(28, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
28.2.f.a	$28$	$2$	28.f	28.f	$6$	$4$	$2$	$0.224$	\(\Q(\zeta_{12})\)	None		✓	✓	✓	28.2.f.a	$4$	$0$	\(-2\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}+\cdots)q^{3}+\cdots\)