Space of modular forms of level 360, weight 4, and Character 360.b

• Label: 360.4.b
• Level: $360$
• Weight: $4$
• Character orbit: 360.b
• Rep. character: $\chi_{360}(251,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	360.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(360, [\chi])\).

	Total	New	Old
Modular forms	224	48	176
Cusp forms	208	48	160
Eisenstein series	16	0	16

Trace form

\( 48 q + 12 q^{4} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(360, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
360.4.b.a	$360$	$4$	360.b	24.f	$2$	$24$	$24$	$21.241$		None		$2$	$0$	\(-6\)	\(0\)	\(-120\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
360.4.b.b	$360$	$4$	360.b	24.f	$2$	$24$	$24$	$21.241$		None		$2$	$0$	\(6\)	\(0\)	\(120\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(360, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)