Space of modular forms of level 120, weight 2, and Character 120.k

• Label: 120.2.k
• Level: $120$
• Weight: $2$
• Character orbit: 120.k
• Rep. character: $\chi_{120}(61,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	120.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(120, [\chi])\).

	Total	New	Old
Modular forms	28	8	20
Cusp forms	20	8	12
Eisenstein series	8	0	8

Trace form

\( 8 q + 4 q^{2} - 2 q^{4} + 2 q^{6} + 8 q^{7} + 4 q^{8} - 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(120, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
120.2.k.a	$120$	$2$	120.k	8.b	$2$	$2$	$2$	$0.958$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+i)q^{2}-iq^{3}+2iq^{4}+iq^{5}+\cdots\)
120.2.k.b	$120$	$2$	120.k	8.b	$2$	$6$	$6$	$0.958$	6.0.399424.1	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(\beta _{1}+\beta _{5})q^{4}+\beta _{1}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(120, [\chi])\) into lower level spaces

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