Space of modular forms of level 28, weight 7, and Character 28.h

• Label: 28.7.h
• Level: $28$
• Weight: $7$
• Character orbit: 28.h
• Rep. character: $\chi_{28}(5,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $28$
• Trace bound: $0$

Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(28, [\chi])\).

	Total	New	Old
Modular forms	54	8	46
Cusp forms	42	8	34
Eisenstein series	12	0	12

Trace form

\( 8 q + 168 q^{5} - 452 q^{7} + 2004 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(28, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
28.7.h.a	$28$	$7$	28.h	7.d	$6$	$8$	$4$	$6.442$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(168\)	\(-452\)	$2^{8}\cdot 3^{4}\cdot 7^{3}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{3}+(28-14\beta _{1}-\beta _{5})q^{5}+(-11^{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(28, [\chi])\) into lower level spaces

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