Space of modular forms of level 840, weight 2, and Character 840.bm

• Label: 840.2.bm
• Level: $840$
• Weight: $2$
• Character orbit: 840.bm
• Rep. character: $\chi_{840}(83,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $368$
• Newform subspaces: $1$
• Sturm bound: $384$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.bm (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 840 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(384\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(840, [\chi])\).

	Total	New	Old
Modular forms	400	400	0
Cusp forms	368	368	0
Eisenstein series	32	32	0

Trace form

\( 368 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(840, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
840.2.bm.a	$840$	$2$	840.bm	840.am	$4$	$368$	$184$	$6.707$		None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$