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

• Label: 120.4.r
• Level: $120$
• Weight: $4$
• Character orbit: 120.r
• Rep. character: $\chi_{120}(17,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $36$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.r (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	160	36	124
Cusp forms	128	36	92
Eisenstein series	32	0	32

Trace form

\( 36 q - 12 q^{7} + O(q^{10}) \)

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.r.a	$120$	$4$	120.r	15.e	$4$	$36$	$18$	$7.080$		None		✓	✓	✓	120.4.r.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{4}^{\mathrm{old}}(120, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)