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

• Label: 120.4.w
• Level: $120$
• Weight: $4$
• Character orbit: 120.w
• Rep. character: $\chi_{120}(53,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $136$
• Newform subspaces: $3$
• Sturm bound: $96$
• Trace bound: $2$

Defining parameters

Level:	$N$	$=$	$120 = 2^{3} \cdot 3 \cdot 5$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	120.w (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$120$
Character field:			$\Q(i)$
Newform subspaces:			$3$
Sturm bound:			$96$
Trace bound:			$2$
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	152	152	0
Cusp forms	136	136	0
Eisenstein series	16	16	0

Trace form

136 * q - 4 * q^6 - 8 * q^7 + 68 * q^10 - 56 * q^12 - 4 * q^15 + 124 * q^16 + 220 * q^18 - 252 * q^22 - 8 * q^25 - 180 * q^28 + 328 * q^30 - 544 * q^31 - 112 * q^33 + 460 * q^36 - 136 * q^40 - 536 * q^42 + 568 * q^46 - 148 * q^48 + 616 * q^52 - 1008 * q^55 - 112 * q^57 - 332 * q^58 - 424 * q^60 + 1368 * q^63 + 304 * q^66 - 1796 * q^70 + 224 * q^72 - 8 * q^73 - 1624 * q^76 - 1448 * q^78 + 1224 * q^81 - 1472 * q^82 - 1184 * q^87 + 2028 * q^88 - 996 * q^90 + 2732 * q^96 - 1496 * q^97

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.w.a	$120$	$4$	120.w	120.w	$4$	$4$	$2$	$7.080$	$\Q(i, \sqrt{6})$	$\Q(\sqrt{-6})$		✓			120.4.w.a	$4$	$0$	$-8$	$0$	$-28$	$68$	$3^{2}$	$\mathrm{U}(1)[D_{4}]$	$q+(-2+2\beta _{2})q^{2}-\beta _{1}q^{3}-8\beta _{2}q^{4}+\cdots$
120.4.w.b	$120$	$4$	120.w	120.w	$4$	$4$	$2$	$7.080$	$\Q(i, \sqrt{6})$	$\Q(\sqrt{-6})$		✓			120.4.w.a	$4$	$0$	$8$	$0$	$28$	$68$	$3^{2}$	$\mathrm{U}(1)[D_{4}]$	$q+(2-2\beta _{2})q^{2}+\beta _{1}q^{3}-8\beta _{2}q^{4}+(7+\cdots)q^{5}+\cdots$
120.4.w.c	$120$	$4$	120.w	120.w	$4$	$128$	$64$	$7.080$		None		✓	✓		120.4.w.c	$8$	$0$	$0$	$0$	$0$	$-144$		$\mathrm{SU}(2)[C_{4}]$