Space of modular forms of level 360, weight 2, and Character 360.bf

• Label: 360.2.bf
• Level: $360$
• Weight: $2$
• Character orbit: 360.bf
• Rep. character: $\chi_{360}(61,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bf (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 72 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(360, [\chi])\).

	Total	New	Old
Modular forms	152	96	56
Cusp forms	136	96	40
Eisenstein series	16	0	16

Trace form

\( 96 q - 6 q^{6} + 12 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(360, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
360.2.bf.a	$360$	$2$	360.bf	72.n	$6$	$4$	$2$	$2.875$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
360.2.bf.b	$360$	$2$	360.bf	72.n	$6$	$92$	$46$	$2.875$		None		$4$	$0$	\(2\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(360, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)