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

• Label: 28.4.e
• Level: $28$
• Weight: $4$
• Character orbit: 28.e
• Rep. character: $\chi_{28}(9,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	28.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(16\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	30	4	26
Cusp forms	18	4	14
Eisenstein series	12	0	12

Trace form

\( 4 q + 14 q^{5} + 24 q^{7} - 20 q^{9} + O(q^{10}) \)

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.e.a	$28$	$4$	28.e	7.c	$3$	$4$	$2$	$1.652$	\(\Q(\sqrt{-3}, \sqrt{37})\)	None		✓	✓	✓	28.4.e.a	$2$	$0$	\(0\)	\(0\)	\(14\)	\(24\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{3}+(7-7\beta _{1}-2\beta _{2}-2\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(28, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(28, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)