Space of modular forms of level 1080, weight 1, and Character 1080.p

• Label: 1080.1.p
• Level: $1080$
• Weight: $1$
• Character orbit: 1080.p
• Rep. character: $\chi_{1080}(379,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $216$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1080.p (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(216\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1080, [\chi])\).

	Total	New	Old
Modular forms	20	4	16
Cusp forms	8	4	4
Eisenstein series	12	0	12

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q - 2 q^{4} + 2 q^{10} - 2 q^{16} + 4 q^{19} + 4 q^{25} - 6 q^{34} - 4 q^{40} - 2 q^{46} - 4 q^{49} + 4 q^{64} - 2 q^{76} - 4 q^{94}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1080, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1080.1.p.a	$1080$	$1$	1080.p	40.e	$2$	$2$	$2$	$0.539$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-15}) \)	None		✓			1080.1.p.a	$4$	$0$	\(-1\)	\(0\)	\(-2\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{5}+q^{8}-\zeta_{6}^{2}q^{10}+\cdots\)
1080.1.p.b	$1080$	$1$	1080.p	40.e	$2$	$2$	$2$	$0.539$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-15}) \)	None		✓			1080.1.p.a	$4$	$0$	\(1\)	\(0\)	\(2\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{5}-q^{8}-\zeta_{6}^{2}q^{10}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1080, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1080, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)