Space of modular forms of level 360, weight 1, and Character 360.p

• Label: 360.1.p
• Level: $360$
• Weight: $1$
• Character orbit: 360.p
• Rep. character: $\chi_{360}(19,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	360.p (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(72\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(360, [\chi])\).

	Total	New	Old
Modular forms	10	4	6
Cusp forms	2	2	0
Eisenstein series	8	2	6

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q + 2 q^{4} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(360, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
360.1.p.a	$360$	$1$	360.p	40.e	$2$	$1$	$1$	$0.180$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \)	\(\Q(\sqrt{6}) \)	✓	$4$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)	$1$		\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+q^{16}+\cdots\)
360.1.p.b	$360$	$1$	360.p	40.e	$2$	$1$	$1$	$0.180$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \)	\(\Q(\sqrt{6}) \)	✓	$4$	$0$	\(1\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{16}+\cdots\)