Space of modular forms of level 120, weight 3, and Character 120.l

• Label: 120.3.l
• Level: $120$
• Weight: $3$
• Character orbit: 120.l
• Rep. character: $\chi_{120}(41,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	120.l (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(120, [\chi])\).

	Total	New	Old
Modular forms	56	8	48
Cusp forms	40	8	32
Eisenstein series	16	0	16

Trace form

\( 8 q - 4 q^{3} + 16 q^{7} + 20 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(120, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
120.3.l.a	$120$	$3$	120.l	3.b	$2$	$8$	$8$	$3.270$	8.0.\(\cdots\).5	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(16\)	$2^{5}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{6}q^{5}+(1+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(120, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(120, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)