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

• Label: 28.3.c
• Level: $28$
• Weight: $3$
• Character orbit: 28.c
• Rep. character: $\chi_{28}(15,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• 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.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
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	10	6	4
Cusp forms	6	6	0
Eisenstein series	4	0	4

Trace form

\( 6 q - q^{2} + q^{4} - 4 q^{5} + 6 q^{6} - 13 q^{8} - 10 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
28.3.c.a	$28$	$3$	28.c	4.b	$2$	$6$	$6$	$0.763$	6.0.1539727.2	None		$2$	$0$	\(-1\)	\(0\)	\(-4\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-\beta _{3}q^{3}+(-\beta _{1}-\beta _{4})q^{4}+\cdots\)