Space of modular forms of level 927, weight 2, and Character 927.w

• Label: 927.2.w
• Level: $927$
• Weight: $2$
• Character orbit: 927.w
• Rep. character: $\chi_{927}(80,\cdot)$
• Character field: $\Q(\zeta_{34})$
• Dimension: $576$
• Newform subspaces: $1$
• Sturm bound: $208$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 927 = 3^{2} \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	927.w (of order \(34\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 309 \)
Character field:			\(\Q(\zeta_{34})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(208\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(927, [\chi])\).

	Total	New	Old
Modular forms	1728	576	1152
Cusp forms	1600	576	1024
Eisenstein series	128	0	128

Trace form

\( 576 q + 40 q^{4} - 16 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(927, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
927.2.w.a	$927$	$2$	927.w	309.k	$34$	$576$	$36$	$7.402$		None		✓	927.2.w.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)		$\mathrm{SU}(2)[C_{34}]$

Decomposition of \(S_{2}^{\mathrm{old}}(927, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(927, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(309, [\chi])\)\(^{\oplus 2}\)