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

• Label: 360.2.bd
• Level: $360$
• Weight: $2$
• Character orbit: 360.bd
• Rep. character: $\chi_{360}(59,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $136$
• 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.bd (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 360 \)
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	152	0
Cusp forms	136	136	0
Eisenstein series	16	16	0

Trace form

\( 136 q - 2 q^{4} - 8 q^{9} + O(q^{10}) \)

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.bd.a	$360$	$2$	360.bd	360.ad	$6$	$8$	$4$	$2.875$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{24}+\zeta_{24}^{6})q^{2}+(-\zeta_{24}^{3}+\zeta_{24}^{4}+\cdots)q^{3}+\cdots\)
360.2.bd.b	$360$	$2$	360.bd	360.ad	$6$	$128$	$64$	$2.875$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$