Space of modular forms of level 28, weight 9, and Character 28.h

• Label: 28.9.h
• Level: $28$
• Weight: $9$
• Character orbit: 28.h
• Rep. character: $\chi_{28}(5,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $10$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
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:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(28, [\chi])\).

	Total	New	Old
Modular forms	70	10	60
Cusp forms	58	10	48
Eisenstein series	12	0	12

Trace form

\( 10 q - 81 q^{3} - 837 q^{5} + 1526 q^{7} + 1902 q^{9} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(28, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
28.9.h.a	$28$	$9$	28.h	7.d	$6$	$10$	$5$	$11.407$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(-81\)	\(-837\)	\(1526\)	$2^{12}\cdot 3^{6}\cdot 7^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-11+5\beta _{1}+\beta _{3})q^{3}+(-57-55\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(28, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(28, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)