Space of modular forms of level 120, weight 4, and Character 120.b

• Label: 120.4.b
• Level: $120$
• Weight: $4$
• Character orbit: 120.b
• Rep. character: $\chi_{120}(11,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(120, [\chi])\).

	Total	New	Old
Modular forms	76	48	28
Cusp forms	68	48	20
Eisenstein series	8	0	8

Trace form

\( 48 q - 6 q^{4} + 30 q^{6} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(120, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
120.4.b.a	$120$	$4$	120.b	24.f	$2$	$24$	$24$	$7.080$		None		✓			120.4.b.a	$2$	$0$	\(-3\)	\(0\)	\(120\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
120.4.b.b	$120$	$4$	120.b	24.f	$2$	$24$	$24$	$7.080$		None		✓			120.4.b.a	$2$	$0$	\(3\)	\(0\)	\(-120\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(120, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(120, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)