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

• Label: 1080.2.d
• Level: $1080$
• Weight: $2$
• Character orbit: 1080.d
• Rep. character: $\chi_{1080}(109,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $10$
• Sturm bound: $432$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(432\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(53\)

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.d.a	$1080$	$2$	1080.d	40.f	$2$	$4$	$4$	$8.624$	\(\Q(\sqrt{-3}, \sqrt{5})\)	\(\Q(\sqrt{-15}) \)		$4$	$0$	\(-3\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+(-1+\beta _{3})q^{2}+(\beta _{2}-\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1080.2.d.b	$1080$	$2$	1080.d	40.f	$2$	$4$	$4$	$8.624$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-30}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{2}-2q^{4}-\beta _{2}q^{5}+2\beta _{1}q^{8}+\cdots\)
1080.2.d.c	$1080$	$2$	1080.d	40.f	$2$	$4$	$4$	$8.624$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-30}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}-2q^{4}-\beta _{2}q^{5}-2\beta _{1}q^{8}+\cdots\)
1080.2.d.d	$1080$	$2$	1080.d	40.f	$2$	$4$	$4$	$8.624$	\(\Q(\sqrt{2}, \sqrt{-3})\)	\(\Q(\sqrt{-6}) \)		$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{3}q^{2}+2q^{4}+(-2-\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)
1080.2.d.e	$1080$	$2$	1080.d	40.f	$2$	$4$	$4$	$8.624$	\(\Q(\sqrt{2}, \sqrt{-3})\)	\(\Q(\sqrt{-6}) \)		$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{3}q^{2}+2q^{4}+(2+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\cdots\)
1080.2.d.f	$1080$	$2$	1080.d	40.f	$2$	$4$	$4$	$8.624$	\(\Q(\sqrt{-3}, \sqrt{5})\)	\(\Q(\sqrt{-15}) \)		$4$	$0$	\(3\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+(1-\beta _{3})q^{2}+(\beta _{2}-\beta _{3})q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
1080.2.d.g	$1080$	$2$	1080.d	40.f	$2$	$16$	$16$	$8.624$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(-2\)	\(0\)	\(-6\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{12}q^{2}+(-1+\beta _{3}+\beta _{5})q^{4}-\beta _{10}q^{5}+\cdots\)
1080.2.d.h	$1080$	$2$	1080.d	40.f	$2$	$16$	$16$	$8.624$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(2\)	\(0\)	\(6\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{12}q^{2}+(-1+\beta _{3}+\beta _{5})q^{4}+\beta _{10}q^{5}+\cdots\)
1080.2.d.i	$1080$	$2$	1080.d	40.f	$2$	$20$	$20$	$8.624$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{2}+\beta _{11}q^{4}+\beta _{14}q^{5}+(\beta _{12}+\cdots)q^{7}+\cdots\)
1080.2.d.j	$1080$	$2$	1080.d	40.f	$2$	$20$	$20$	$8.624$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{14}q^{5}+(1-\beta _{3}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1080, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 3}\)