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

• Label: 1080.4.f
• Level: $1080$
• Weight: $4$
• Character orbit: 1080.f
• Rep. character: $\chi_{1080}(649,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $4$
• Sturm bound: $864$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1080.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(864\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	672	72	600
Cusp forms	624	72	552
Eisenstein series	48	0	48

Trace form

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

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.f.a	$1080$	$4$	1080.f	5.b	$2$	$16$	$16$	$63.722$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{24}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{9}-\beta _{10})q^{5}+\beta _{4}q^{7}+(\beta _{8}-\beta _{9}+\cdots)q^{11}+\cdots\)
1080.4.f.b	$1080$	$4$	1080.f	5.b	$2$	$18$	$18$	$63.722$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{16}\cdot 3^{10}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{5}-\beta _{6})q^{5}+(2\beta _{5}-\beta _{9})q^{7}+(-3+\cdots)q^{11}+\cdots\)
1080.4.f.c	$1080$	$4$	1080.f	5.b	$2$	$18$	$18$	$63.722$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{16}\cdot 3^{10}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{5}+\beta _{6})q^{5}+(2\beta _{5}-\beta _{9})q^{7}+(3+\beta _{3}+\cdots)q^{11}+\cdots\)
1080.4.f.d	$1080$	$4$	1080.f	5.b	$2$	$20$	$20$	$63.722$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{25}\cdot 3^{12}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{5}-\beta _{8}q^{7}-\beta _{13}q^{11}-\beta _{19}q^{13}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(1080, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)