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

• Label: 120.3.u
• Level: $120$
• Weight: $3$
• Character orbit: 120.u
• Rep. character: $\chi_{120}(73,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	120.u (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(72\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	112	12	100
Cusp forms	80	12	68
Eisenstein series	32	0	32

Trace form

12 * q - 8 * q^5 - 8 * q^7 + 16 * q^11 + 44 * q^13 + 24 * q^15 + 28 * q^17 - 96 * q^23 - 68 * q^25 + 16 * q^31 + 72 * q^33 + 52 * q^37 - 208 * q^41 - 96 * q^43 - 36 * q^45 - 32 * q^47 - 12 * q^53 + 136 * q^55 - 96 * q^57 + 240 * q^61 - 24 * q^63 + 20 * q^65 - 224 * q^67 + 32 * q^71 - 100 * q^73 + 96 * q^75 + 240 * q^77 - 108 * q^81 + 608 * q^83 + 60 * q^85 + 360 * q^87 + 256 * q^91 + 144 * q^93 - 32 * q^95 - 356 * q^97

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
120.3.u.a	$120$	$3$	120.u	5.c	$4$	$4$	$2$	$3.270$	\(\Q(i, \sqrt{6})\)	None		✓			120.3.u.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{3}+(1+\beta _{1}+3\beta _{2}-2\beta _{3})q^{5}+\cdots\)
120.3.u.b	$120$	$3$	120.u	5.c	$4$	$8$	$4$	$3.270$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓	✓		120.3.u.b	$2$	$0$	\(0\)	\(0\)	\(-12\)	\(4\)	$2\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{1}q^{3}+(-2+\beta _{1}+\beta _{6})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(120, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)