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

• Label: 120.4.d
• Level: $120$
• Weight: $4$
• Character orbit: 120.d
• Rep. character: $\chi_{120}(109,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• 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.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(13\)

Dimensions

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

	Total	New	Old
Modular forms	76	36	40
Cusp forms	68	36	32
Eisenstein series	8	0	8

Trace form

\( 36 q - 6 q^{4} - 6 q^{6} + 324 q^{9} + O(q^{10}) \)

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.d.a	$120$	$4$	120.d	40.f	$2$	$18$	$18$	$7.080$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		✓			120.4.d.a	$2$	$0$	\(-1\)	\(54\)	\(0\)	\(0\)	$2^{25}\cdot 3^{4}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+3q^{3}+\beta _{2}q^{4}+\beta _{10}q^{5}+\cdots\)
120.4.d.b	$120$	$4$	120.d	40.f	$2$	$18$	$18$	$7.080$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		✓			120.4.d.a	$2$	$0$	\(1\)	\(-54\)	\(0\)	\(0\)	$2^{25}\cdot 3^{4}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}-3q^{3}-\beta _{7}q^{4}+\beta _{11}q^{5}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(120, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)