Space of modular forms of level 945, weight 2, and Character 945.cs

• Label: 945.2.cs
• Level: $945$
• Weight: $2$
• Character orbit: 945.cs
• Rep. character: $\chi_{945}(104,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $840$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.cs (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 945 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(945, [\chi])\).

	Total	New	Old
Modular forms	888	888	0
Cusp forms	840	840	0
Eisenstein series	48	48	0

Trace form

\( 840 q - 24 q^{4} - 30 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(945, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
945.2.cs.a	$945$	$2$	945.cs	945.bs	$18$	$24$	$4$	$7.546$		\(\Q(\sqrt{-35}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{18}]$
945.2.cs.b	$945$	$2$	945.cs	945.bs	$18$	$816$	$136$	$7.546$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$