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

• Label: 1080.2.b
• Level: $1080$
• Weight: $2$
• Character orbit: 1080.b
• Rep. character: $\chi_{1080}(971,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $4$
• Sturm bound: $432$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(432\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(7\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	228	64	164
Cusp forms	204	64	140
Eisenstein series	24	0	24

Trace form

64 * q + 2 * q^4 - 2 * q^10 + 34 * q^16 - 8 * q^19 - 20 * q^22 + 64 * q^25 + 44 * q^28 + 30 * q^34 + 16 * q^40 + 62 * q^46 - 80 * q^49 + 4 * q^52 - 16 * q^58 - 16 * q^64 + 128 * q^67 + 12 * q^70 - 16 * q^73 + 6 * q^76 - 44 * q^82 - 20 * q^88 + 48 * q^91 - 44 * q^94 + 16 * q^97

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.b.a	$1080$	$2$	1080.b	24.f	$2$	$16$	$16$	$8.624$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			1080.2.b.a	$2$	$0$	\(-2\)	\(0\)	\(16\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-\beta _{6}q^{4}+q^{5}-\beta _{4}q^{7}-\beta _{7}q^{8}+\cdots\)
1080.2.b.b	$1080$	$2$	1080.b	24.f	$2$	$16$	$16$	$8.624$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			1080.2.b.b	$2$	$0$	\(-1\)	\(0\)	\(-16\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}+\beta _{4}q^{4}-q^{5}-\beta _{2}q^{7}+\beta _{1}q^{8}+\cdots\)
1080.2.b.c	$1080$	$2$	1080.b	24.f	$2$	$16$	$16$	$8.624$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			1080.2.b.b	$2$	$0$	\(1\)	\(0\)	\(16\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}+\beta _{4}q^{4}+q^{5}-\beta _{2}q^{7}-\beta _{1}q^{8}+\cdots\)
1080.2.b.d	$1080$	$2$	1080.b	24.f	$2$	$16$	$16$	$8.624$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			1080.2.b.a	$2$	$0$	\(2\)	\(0\)	\(-16\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-\beta _{6}q^{4}-q^{5}-\beta _{4}q^{7}+\beta _{7}q^{8}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1080, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)