Space of modular forms of level 1080, weight 2, and Character 1080.m

• Label: 1080.2.m
• Level: $1080$
• Weight: $2$
• Character orbit: 1080.m
• Rep. character: $\chi_{1080}(539,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $3$
• Sturm bound: $432$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 120 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(432\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1080, [\chi])\).

	Total	New	Old
Modular forms	228	96	132
Cusp forms	204	96	108
Eisenstein series	24	0	24

Trace form

\( 96 q + 2 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1080, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1080.2.m.a	$1080$	$2$	1080.m	120.m	$2$	$8$	$8$	$8.624$	8.0.12960000.1	\(\Q(\sqrt{-15}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{3}q^{2}+\beta _{1}q^{4}+(\beta _{3}+\beta _{6})q^{5}+(-\beta _{2}+\cdots)q^{8}+\cdots\)
1080.2.m.b	$1080$	$2$	1080.m	120.m	$2$	$40$	$40$	$8.624$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1080.2.m.c	$1080$	$2$	1080.m	120.m	$2$	$48$	$48$	$8.624$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1080, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1080, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)