Space of modular forms of level 28, weight 3, and Character 28.g

• Label: 28.3.g
• Level: $28$
• Weight: $3$
• Character orbit: 28.g
• Rep. character: $\chi_{28}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	28.g (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(28, [\chi])\).

	Total	New	Old
Modular forms	20	20	0
Cusp forms	12	12	0
Eisenstein series	8	8	0

Trace form

12 * q - 2 * q^2 - 4 * q^4 - 2 * q^5 - 12 * q^6 - 8 * q^8 + 4 * q^9 - 2 * q^10 - 24 * q^12 - 24 * q^13 + 2 * q^14 + 16 * q^16 - 2 * q^17 + 56 * q^18 + 152 * q^20 - 78 * q^21 + 44 * q^22 - 44 * q^24 + 56 * q^26 + 8 * q^28 + 72 * q^29 - 74 * q^30 - 112 * q^32 - 14 * q^33 - 316 * q^34 - 160 * q^36 + 86 * q^37 - 2 * q^38 - 148 * q^40 + 8 * q^41 + 68 * q^42 + 64 * q^44 + 156 * q^45 + 162 * q^46 + 512 * q^48 + 108 * q^49 + 208 * q^50 - 64 * q^52 - 74 * q^53 + 182 * q^54 + 16 * q^56 - 220 * q^57 - 176 * q^58 - 232 * q^60 + 86 * q^61 - 532 * q^62 - 160 * q^64 - 140 * q^65 + 102 * q^66 - 68 * q^68 - 300 * q^69 + 90 * q^70 + 152 * q^72 - 234 * q^73 + 290 * q^74 + 576 * q^76 - 262 * q^77 + 64 * q^78 + 146 * q^81 + 272 * q^82 - 28 * q^84 + 268 * q^85 - 16 * q^86 - 188 * q^88 + 6 * q^89 - 640 * q^90 - 448 * q^92 + 162 * q^93 + 102 * q^94 - 320 * q^96 + 744 * q^97 - 190 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(28, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
28.3.g.a	$28$	$3$	28.g	28.g	$6$	$12$	$6$	$0.763$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓	✓	28.3.g.a	$4$	$0$	\(-2\)	\(0\)	\(-2\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{6}q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\beta _{5}+\beta _{9}+\cdots)q^{4}+\cdots\)