Space of modular forms of level 1080, weight 4, and Character 1080.q

• Label: 1080.4.q
• Level: $1080$
• Weight: $4$
• Character orbit: 1080.q
• Rep. character: $\chi_{1080}(361,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $72$
• Newform subspaces: $5$
• Sturm bound: $864$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1080.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(864\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1080, [\chi])\).

	Total	New	Old
Modular forms	1344	72	1272
Cusp forms	1248	72	1176
Eisenstein series	96	0	96

Trace form

\( 72 q - 10 q^{5} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1080, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1080.4.q.a	$1080$	$4$	1080.q	9.c	$3$	$2$	$1$	$63.722$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(5\)	\(23\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+5\zeta_{6}q^{5}+(23-23\zeta_{6})q^{7}+(-48+\cdots)q^{11}+\cdots\)
1080.4.q.b	$1080$	$4$	1080.q	9.c	$3$	$16$	$8$	$63.722$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(40\)	\(-34\)	$2^{10}\cdot 3^{14}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(5-5\beta _{1})q^{5}+(-4\beta _{1}+\beta _{5})q^{7}+(8\beta _{1}+\cdots)q^{11}+\cdots\)
1080.4.q.c	$1080$	$4$	1080.q	9.c	$3$	$16$	$8$	$63.722$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(40\)	\(-31\)	$2^{12}\cdot 3^{16}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(5-5\beta _{1})q^{5}+(-4\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
1080.4.q.d	$1080$	$4$	1080.q	9.c	$3$	$18$	$9$	$63.722$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-45\)	\(20\)	$2^{20}\cdot 3^{16}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-5-5\beta _{1})q^{5}+(-2\beta _{1}+\beta _{12})q^{7}+\cdots\)
1080.4.q.e	$1080$	$4$	1080.q	9.c	$3$	$20$	$10$	$63.722$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-50\)	\(22\)	$2^{22}\cdot 3^{25}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-5+5\beta _{2})q^{5}+(2\beta _{2}+\beta _{3})q^{7}+(-5\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(1080, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1080, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)