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

• Label: 120.4.w
• Level: $120$
• Weight: $4$
• Character orbit: 120.w
• Rep. character: $\chi_{120}(53,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $136$
• Newform subspaces: $3$
• Sturm bound: $96$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.w (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 120 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(96\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	152	152	0
Cusp forms	136	136	0
Eisenstein series	16	16	0

Trace form

\( 136 q - 4 q^{6} - 8 q^{7} + O(q^{10}) \)

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.w.a	$120$	$4$	120.w	120.w	$4$	$4$	$2$	$7.080$	\(\Q(i, \sqrt{6})\)	\(\Q(\sqrt{-6}) \)		✓			120.4.w.a	$4$	$0$	\(-8\)	\(0\)	\(-28\)	\(68\)	$3^{2}$	$\mathrm{U}(1)[D_{4}]$	\(q+(-2+2\beta _{2})q^{2}-\beta _{1}q^{3}-8\beta _{2}q^{4}+\cdots\)
120.4.w.b	$120$	$4$	120.w	120.w	$4$	$4$	$2$	$7.080$	\(\Q(i, \sqrt{6})\)	\(\Q(\sqrt{-6}) \)		✓			120.4.w.a	$4$	$0$	\(8\)	\(0\)	\(28\)	\(68\)	$3^{2}$	$\mathrm{U}(1)[D_{4}]$	\(q+(2-2\beta _{2})q^{2}+\beta _{1}q^{3}-8\beta _{2}q^{4}+(7+\cdots)q^{5}+\cdots\)
120.4.w.c	$120$	$4$	120.w	120.w	$4$	$128$	$64$	$7.080$		None		✓	✓		120.4.w.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-144\)		$\mathrm{SU}(2)[C_{4}]$