Space of modular forms of level 28, weight 11, and Character 28.b

• Label: 28.11.b
• Level: $28$
• Weight: $11$
• Character orbit: 28.b
• Rep. character: $\chi_{28}(13,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $44$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	28.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(44\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(28, [\chi])\).

	Total	New	Old
Modular forms	43	6	37
Cusp forms	37	6	31
Eisenstein series	6	0	6

Trace form

\( 6 q - 15666 q^{7} - 208122 q^{9} + O(q^{10}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(28, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
28.11.b.a	$28$	$11$	28.b	7.b	$2$	$6$	$6$	$17.790$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-15666\)	$2^{19}\cdot 3^{2}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-5\beta _{1}-\beta _{2})q^{5}+(-2611+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(28, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(28, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)