Space of modular forms of level 931, weight 2, and Character 931.bz

• Label: 931.2.bz
• Level: $931$
• Weight: $2$
• Character orbit: 931.bz
• Rep. character: $\chi_{931}(12,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $1104$
• Newform subspaces: $1$
• Sturm bound: $186$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.bz (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 931 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(186\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(931, [\chi])\).

	Total	New	Old
Modular forms	1152	1152	0
Cusp forms	1104	1104	0
Eisenstein series	48	48	0

Trace form

\( 1104 q - 21 q^{2} - 18 q^{3} + 179 q^{4} - 7 q^{5} - 19 q^{6} - 24 q^{7} + 82 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(931, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
931.2.bz.a	$931$	$2$	931.bz	931.az	$42$	$1104$	$92$	$7.434$		None		$2$	$0$	\(-21\)	\(-18\)	\(-7\)	\(-24\)		$\mathrm{SU}(2)[C_{42}]$