Space of modular forms of level 147, weight 4, and Character 147.o

• Label: 147.4.o
• Level: $147$
• Weight: $4$
• Character orbit: 147.o
• Rep. character: $\chi_{147}(5,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $648$
• Newform subspaces: $1$
• Sturm bound: $74$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.o (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 147 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(74\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(147, [\chi])\).

	Total	New	Old
Modular forms	696	696	0
Cusp forms	648	648	0
Eisenstein series	48	48	0

Trace form

\( 648 q - 11 q^{3} - 234 q^{4} + 14 q^{6} + 28 q^{7} - 125 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(147, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
147.4.o.a	$147$	$4$	147.o	147.o	$42$	$648$	$54$	$8.673$		None		$4$	$0$	\(0\)	\(-11\)	\(0\)	\(28\)		$\mathrm{SU}(2)[C_{42}]$