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

• Label: 120.4.f
• Level: $120$
• Weight: $4$
• Character orbit: 120.f
• Rep. character: $\chi_{120}(49,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $4$
• Sturm bound: $96$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(96\)
Trace bound:			\(5\)
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	80	10	70
Cusp forms	64	10	54
Eisenstein series	16	0	16

Trace form

\( 10 q + 8 q^{5} - 90 q^{9} + O(q^{10}) \)

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.f.a	$120$	$4$	120.f	5.b	$2$	$2$	$2$	$7.080$	\(\Q(\sqrt{-1}) \)	None		✓			120.4.f.a	$2$	$1$	\(0\)	\(0\)	\(-20\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+(-10+5i)q^{5}-10iq^{7}+\cdots\)
120.4.f.b	$120$	$4$	120.f	5.b	$2$	$2$	$2$	$7.080$	\(\Q(\sqrt{-1}) \)	None		✓			120.4.f.b	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+(-2-11i)q^{5}-10iq^{7}+\cdots\)
120.4.f.c	$120$	$4$	120.f	5.b	$2$	$2$	$2$	$7.080$	\(\Q(\sqrt{-1}) \)	None		✓			120.4.f.c	$2$	$0$	\(0\)	\(0\)	\(10\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+(5+10i)q^{5}+4iq^{7}-9q^{9}+\cdots\)
120.4.f.d	$120$	$4$	120.f	5.b	$2$	$4$	$4$	$7.080$	\(\Q(i, \sqrt{129})\)	None		✓	✓		120.4.f.d	$2$	$0$	\(0\)	\(0\)	\(22\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta _{1}q^{3}+(6+5\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(120, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)