Space of modular forms of level 946, weight 2, and Character 946.z

• Label: 946.2.z
• Level: $946$
• Weight: $2$
• Character orbit: 946.z
• Rep. character: $\chi_{946}(39,\cdot)$
• Character field: $\Q(\zeta_{70})$
• Dimension: $1056$
• Newform subspaces: $2$
• Sturm bound: $264$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.z (of order \(70\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 473 \)
Character field:			\(\Q(\zeta_{70})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(264\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(946, [\chi])\).

	Total	New	Old
Modular forms	3264	1056	2208
Cusp forms	3072	1056	2016
Eisenstein series	192	0	192

Trace form

\( 1056 q + 44 q^{4} - 10 q^{6} - 40 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(946, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
946.2.z.a	$946$	$2$	946.z	473.ab	$70$	$528$	$22$	$7.554$		None		$2$	$0$	\(-22\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{70}]$
946.2.z.b	$946$	$2$	946.z	473.ab	$70$	$528$	$22$	$7.554$		None		$2$	$0$	\(22\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{70}]$

Decomposition of \(S_{2}^{\mathrm{old}}(946, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(946, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(473, [\chi])\)\(^{\oplus 2}\)