Space of modular forms of level 28, weight 4, and Character 28.d

• Label: 28.4.d
• Level: $28$
• Weight: $4$
• Character orbit: 28.d
• Rep. character: $\chi_{28}(27,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $2$
• Sturm bound: $16$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	28.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(16\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(28, [\chi])\).

	Total	New	Old
Modular forms	14	14	0
Cusp forms	10	10	0
Eisenstein series	4	4	0

Trace form

10 * q - 3 * q^2 - 7 * q^4 - 27 * q^8 + 50 * q^9 - 103 * q^14 + 17 * q^16 - 47 * q^18 - 64 * q^21 + 310 * q^22 - 222 * q^25 + 197 * q^28 - 260 * q^29 + 256 * q^30 + 877 * q^32 - 1219 * q^36 + 492 * q^37 - 1024 * q^42 - 834 * q^44 - 1390 * q^46 + 794 * q^49 + 2313 * q^50 + 12 * q^53 + 1633 * q^56 - 192 * q^57 + 270 * q^58 + 2944 * q^60 - 4327 * q^64 + 448 * q^65 - 3200 * q^70 - 1319 * q^72 - 2746 * q^74 - 612 * q^77 + 7680 * q^78 - 3526 * q^81 + 4480 * q^84 + 1024 * q^85 + 1654 * q^86 + 4966 * q^88 - 6678 * q^92 - 2304 * q^93 - 4859 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(28, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
28.4.d.a	$28$	$4$	28.d	28.d	$2$	$2$	$2$	$1.652$	\(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{-7}) \)		✓			28.4.d.a	$4$	$0$	\(5\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(3-\beta )q^{2}+(7-5\beta )q^{4}+(-7+14\beta )q^{7}+\cdots\)
28.4.d.b	$28$	$4$	28.d	28.d	$2$	$8$	$8$	$1.652$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓	✓		28.4.d.b	$4$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots\)