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

• Label: 1080.2.f
• Level: $1080$
• Weight: $2$
• Character orbit: 1080.f
• Rep. character: $\chi_{1080}(649,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $7$
• Sturm bound: $432$
• Trace bound: $5$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	240	24	216
Cusp forms	192	24	168
Eisenstein series	48	0	48

Trace form

\( 24 q + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1080.2.f.a	$1080$	$2$	1080.f	5.b	$2$	$2$	$2$	$8.624$	\(\Q(\sqrt{-1}) \)	None		✓			1080.2.f.a	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i-2)q^{5}+2 i q^{7}-2 q^{11}+2 i q^{13}+\cdots\)
1080.2.f.b	$1080$	$2$	1080.f	5.b	$2$	$2$	$2$	$8.624$	\(\Q(\sqrt{-1}) \)	None		✓			1080.2.f.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2 i-1)q^{5}+4 i q^{7}-q^{11}+\cdots\)
1080.2.f.c	$1080$	$2$	1080.f	5.b	$2$	$2$	$2$	$8.624$	\(\Q(\sqrt{-1}) \)	None		✓			1080.2.f.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2 i+1)q^{5}+4 i q^{7}+q^{11}+i q^{13}+\cdots\)
1080.2.f.d	$1080$	$2$	1080.f	5.b	$2$	$2$	$2$	$8.624$	\(\Q(\sqrt{-1}) \)	None		✓			1080.2.f.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-i+2)q^{5}+2 i q^{7}+2 q^{11}+\cdots\)
1080.2.f.e	$1080$	$2$	1080.f	5.b	$2$	$4$	$4$	$8.624$	\(\Q(i, \sqrt{6})\)	None		✓			1080.2.f.e	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{2}+\beta _{3})q^{5}-\beta _{2}q^{7}+(2-\beta _{1}+\cdots)q^{11}+\cdots\)
1080.2.f.f	$1080$	$2$	1080.f	5.b	$2$	$4$	$4$	$8.624$	\(\Q(i, \sqrt{6})\)	None		✓			1080.2.f.e	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{2}-\beta _{3})q^{5}-\beta _{2}q^{7}+(-2+\beta _{1}+\cdots)q^{11}+\cdots\)
1080.2.f.g	$1080$	$2$	1080.f	5.b	$2$	$8$	$8$	$8.624$	8.0.2702336256.1	None		✓	✓		1080.2.f.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}-\beta _{1}q^{7}+(-2\beta _{3}-\beta _{6}+2\beta _{7})q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1080, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)