Space of modular forms of level 720, weight 6, and Character 720.h

• Label: 720.6.h
• Level: $720$
• Weight: $6$
• Character orbit: 720.h
• Rep. character: $\chi_{720}(431,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $2$
• Sturm bound: $864$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	720.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(864\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(720, [\chi])\).

	Total	New	Old
Modular forms	744	40	704
Cusp forms	696	40	656
Eisenstein series	48	0	48

Trace form

\( 40 q + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(720, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
720.6.h.a	$720$	$6$	720.h	12.b	$2$	$16$	$16$	$115.476$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{42}\cdot 3^{24}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}+\beta _{2}q^{7}-\beta _{7}q^{11}+(70+\beta _{1}+\cdots)q^{13}+\cdots\)
720.6.h.b	$720$	$6$	720.h	12.b	$2$	$24$	$24$	$115.476$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{6}^{\mathrm{old}}(720, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(720, [\chi]) \cong \)