Space of modular forms of level 120, weight 6, and Character 120.f

• Label: 120.6.f
• Level: $120$
• Weight: $6$
• Character orbit: 120.f
• Rep. character: $\chi_{120}(49,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	120.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(120, [\chi])\).

	Total	New	Old
Modular forms	128	14	114
Cusp forms	112	14	98
Eisenstein series	16	0	16

Trace form

\( 14 q - 16 q^{5} - 1134 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(120, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
120.6.f.a	$120$	$6$	120.f	5.b	$2$	$6$	$6$	$19.246$	6.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(50\)	\(0\)	$2^{4}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+9\beta _{1}q^{3}+(8-9\beta _{1}+\beta _{3}-2\beta _{5})q^{5}+\cdots\)
120.6.f.b	$120$	$6$	120.f	5.b	$2$	$8$	$8$	$19.246$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-66\)	\(0\)	$2^{10}\cdot 3^{2}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+9\beta _{1}q^{3}+(-8+10\beta _{1}+\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(120, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(120, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)