Space of modular forms of level 935, weight 2, and Character 935.cf

• Label: 935.2.cf
• Level: $935$
• Weight: $2$
• Character orbit: 935.cf
• Rep. character: $\chi_{935}(2,\cdot)$
• Character field: $\Q(\zeta_{40})$
• Dimension: $1664$
• Newform subspaces: $1$
• Sturm bound: $216$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.cf (of order \(40\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 935 \)
Character field:			\(\Q(\zeta_{40})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(216\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(935, [\chi])\).

	Total	New	Old
Modular forms	1792	1792	0
Cusp forms	1664	1664	0
Eisenstein series	128	128	0

Trace form

\( 1664 q - 12 q^{3} - 400 q^{4} - 20 q^{5} - 40 q^{6} - 40 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(935, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
935.2.cf.a	$935$	$2$	935.cf	935.bf	$40$	$1664$	$104$	$7.466$		None		$4$	$0$	\(0\)	\(-12\)	\(-20\)	\(-40\)		$\mathrm{SU}(2)[C_{40}]$