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

• Label: 935.2.b
• Level: $935$
• Weight: $2$
• Character orbit: 935.b
• Rep. character: $\chi_{935}(749,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $2$
• Sturm bound: $216$
• Trace bound: $1$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	112	80	32
Cusp forms	104	80	24
Eisenstein series	8	0	8

Trace form

\( 80 q - 80 q^{4} + 2 q^{5} - 8 q^{6} - 76 q^{9} + O(q^{10}) \)

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.b.a	$935$	$2$	935.b	5.b	$2$	$36$	$36$	$7.466$		None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
935.2.b.b	$935$	$2$	935.b	5.b	$2$	$44$	$44$	$7.466$		None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(935, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(935, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 2}\)