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

• Label: 360.2.f
• Level: $360$
• Weight: $2$
• Character orbit: 360.f
• Rep. character: $\chi_{360}(289,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $4$
• Sturm bound: $144$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(144\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	88	8	80
Cusp forms	56	8	48
Eisenstein series	32	0	32

Trace form

\( 8 q - 2 q^{5} + O(q^{10}) \)

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.f.a	$360$	$2$	360.f	5.b	$2$	$2$	$2$	$2.875$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2+i)q^{5}+2iq^{7}-2q^{11}+2iq^{13}+\cdots\)
360.2.f.b	$360$	$2$	360.f	5.b	$2$	$2$	$2$	$2.875$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2+i)q^{5}-4iq^{7}+4q^{11}-4iq^{13}+\cdots\)
360.2.f.c	$360$	$2$	360.f	5.b	$2$	$2$	$2$	$2.875$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+i)q^{5}-iq^{7}+4q^{11}+2iq^{13}+\cdots\)
360.2.f.d	$360$	$2$	360.f	5.b	$2$	$2$	$2$	$2.875$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2+i)q^{5}+4iq^{7}-4q^{11}+4iq^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)