Space of modular forms of level 945, weight 1, and Character 945.n

• Label: 945.1.n
• Level: $945$
• Weight: $1$
• Character orbit: 945.n
• Rep. character: $\chi_{945}(188,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	945.n (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(945, [\chi])\).

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

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	8	0

Trace form

\( 8 q - 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(945, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
945.1.n.a	$945$	$1$	945.n	105.k	$4$	$4$	$2$	$0.472$	\(\Q(\zeta_{8})\)	$S_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$		\(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{3}q^{5}-q^{7}-\zeta_{8}q^{8}+\cdots\)
945.1.n.b	$945$	$1$	945.n	105.k	$4$	$4$	$2$	$0.472$	\(\Q(\zeta_{8})\)	$S_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{3}q^{5}-\zeta_{8}^{2}q^{7}+\zeta_{8}q^{8}+\cdots\)