Space of modular forms of level 547, weight 4, and trivial character

• Label: 547.4.a
• Level: $547$
• Weight: $4$
• Character orbit: 547.a
• Rep. character: $\chi_{547}(1,\cdot)$
• Character field: $\Q$
• Dimension: $136$
• Newform subspaces: $2$
• Sturm bound: $182$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(182\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(547))\).

	Total	New	Old
Modular forms	138	136	2
Cusp forms	136	136	0
Eisenstein series	2	0	2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(547\)	Dim
\(+\)	\(71\)
\(-\)	\(65\)

Trace form

\( 136 q + 2 q^{2} - 4 q^{3} + 528 q^{4} + 8 q^{5} - 8 q^{7} + 24 q^{8} + 1206 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(547))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		547
547.4.a.a	$547$	$4$	547.a	1.a	$1$	$65$	$65$	$32.274$		None	✓	$1$	$1$	\(-12\)	\(-35\)	\(-151\)	\(-74\)		$-$	$-$		$\mathrm{SU}(2)$
547.4.a.b	$547$	$4$	547.a	1.a	$1$	$71$	$71$	$32.274$		None	✓	$1$	$0$	\(14\)	\(31\)	\(159\)	\(66\)		$+$	$+$		$\mathrm{SU}(2)$