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 - 2 * q^10 - 12 * q^14 - 4 * q^15 + 2 * q^16 - 4 * q^18 - 8 * q^20 - 12 * q^22 - 16 * q^23 + 10 * q^24 - 8 * q^25 + 28 * q^26 - 28 * q^28 + 8 * q^31 + 4 * q^32 + 2 * q^36 + 2 * q^40 + 12 * q^42 + 12 * q^44 - 28 * q^46 + 16 * q^48 + 24 * q^49 - 4 * q^50 - 8 * q^52 - 2 * q^54 + 16 * q^55 - 4 * q^56 - 16 * q^57 - 12 * q^58 + 2 * q^60 + 24 * q^62 - 8 * q^63 + 22 * q^64 + 4 * q^66 - 16 * q^68 + 4 * q^70 - 16 * q^71 - 4 * q^72 - 16 * q^73 + 20 * q^74 + 28 * q^76 + 8 * q^78 + 8 * q^79 + 16 * q^80 + 8 * q^81 + 48 * q^82 - 12 * q^84 - 24 * q^86 + 24 * q^87 + 28 * q^88 + 2 * q^90 - 24 * q^92 - 4 * q^94 - 18 * q^96 + 16 * q^97 - 12 * q^98

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
120.2.k.a	$120$	$2$	120.k	8.b	$2$	$2$	$2$	$0.958$	\(\Q(\sqrt{-1}) \)	None		✓			120.2.k.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i+1)q^{2}-i q^{3}+2 i q^{4}+i q^{5}+\cdots\)
120.2.k.b	$120$	$2$	120.k	8.b	$2$	$6$	$6$	$0.958$	6.0.399424.1	None		✓	✓		120.2.k.b	$2$	$0$	\(2\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(\beta _{1}+\beta _{5})q^{4}+\beta _{1}q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(120, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)