Space of modular forms of level 547, weight 2, and Character 547.h

• Label: 547.2.h
• Level: $547$
• Weight: $2$
• Character orbit: 547.h
• Rep. character: $\chi_{547}(13,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $540$
• Newform subspaces: $1$
• Sturm bound: $91$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.h (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 547 \)
Character field:			\(\Q(\zeta_{21})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(91\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(547, [\chi])\).

	Total	New	Old
Modular forms	564	564	0
Cusp forms	540	540	0
Eisenstein series	24	24	0

Trace form

\( 540 q - 13 q^{2} - 10 q^{3} + 33 q^{4} - 15 q^{5} + 10 q^{6} - 2 q^{7} - 26 q^{8} - 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(547, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
547.2.h.a	$547$	$2$	547.h	547.h	$21$	$540$	$45$	$4.368$		None		$2$	$0$	\(-13\)	\(-10\)	\(-15\)	\(-2\)		$\mathrm{SU}(2)[C_{21}]$