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

• Label: 120.4.m
• Level: $120$
• Weight: $4$
• Character orbit: 120.m
• Rep. character: $\chi_{120}(59,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 120 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	76	76	0
Cusp forms	68	68	0
Eisenstein series	8	8	0

Trace form

68 * q - 10 * q^4 - 18 * q^6 - 4 * q^9 - 22 * q^10 - 142 * q^16 + 16 * q^19 - 254 * q^24 - 4 * q^25 - 248 * q^30 + 456 * q^34 - 14 * q^36 - 394 * q^40 - 104 * q^46 + 2148 * q^49 - 112 * q^51 + 506 * q^54 - 714 * q^60 + 614 * q^64 - 176 * q^66 + 672 * q^70 - 1600 * q^75 - 1304 * q^76 + 612 * q^81 - 736 * q^84 - 82 * q^90 - 2752 * q^91 + 2056 * q^94 - 1034 * q^96 + 256 * q^99

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.m.a	$120$	$4$	120.m	120.m	$2$	$4$	$4$	$7.080$	\(\Q(\sqrt{3}, \sqrt{-5})\)	\(\Q(\sqrt{-15}) \)		✓			120.4.m.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{3}q^{2}+(-\beta _{1}+2\beta _{3})q^{3}+(6+\beta _{2}+\cdots)q^{4}+\cdots\)
120.4.m.b	$120$	$4$	120.m	120.m	$2$	$64$	$64$	$7.080$		None		✓	✓		120.4.m.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$