Space of modular forms of level 720, weight 1, and Character 720.bk

• Label: 720.1.bk
• Level: $720$
• Weight: $1$
• Character orbit: 720.bk
• Rep. character: $\chi_{720}(143,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	720.bk (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 60 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(720, [\chi])\).

	Total	New	Old
Modular forms	64	4	60
Cusp forms	16	4	12
Eisenstein series	48	0	48

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(720, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
720.1.bk.a	$720$	$1$	720.bk	60.l	$4$	$4$	$2$	$0.359$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{8}q^{5}+(1-\zeta_{8}^{2})q^{13}-\zeta_{8}^{3}q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(720, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(720, [\chi]) \cong \)