Space of modular forms of level 1140, weight 2, and Character 1140.bk

• Label: 1140.2.bk
• Level: $1140$
• Weight: $2$
• Character orbit: 1140.bk
• Rep. character: $\chi_{1140}(221,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $56$
• Newform subspaces: $1$
• Sturm bound: $480$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1140.bk (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(480\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1140, [\chi])\).

	Total	New	Old
Modular forms	504	56	448
Cusp forms	456	56	400
Eisenstein series	48	0	48

Trace form

\( 56 q + 6 q^{3} + 8 q^{7} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1140, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1140.2.bk.a	$1140$	$2$	1140.bk	57.f	$6$	$56$	$28$	$9.103$		None		$4$	$0$	\(0\)	\(6\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1140, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1140, [\chi]) \cong \)