Space of modular forms of level 2268, weight 1, and Character 2268.s

• Label: 2268.1.s
• Level: $2268$
• Weight: $1$
• Character orbit: 2268.s
• Rep. character: $\chi_{2268}(755,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $7$
• Sturm bound: $432$
• Trace bound: $28$

Defining parameters

Level:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2268.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 252 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(432\)
Trace bound:			\(28\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2268, [\chi])\).

	Total	New	Old
Modular forms	80	40	40
Cusp forms	32	32	0
Eisenstein series	48	8	40

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	32	0	0	0

Trace form

\( 32 q - 4 q^{4} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2268, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2268.1.s.a	$2268$	$1$	2268.s	252.s	$6$	$2$	$1$	$1.132$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-21}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(-1\)	\(1\)	$1$		\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots\)
2268.1.s.b	$2268$	$1$	2268.s	252.s	$6$	$2$	$1$	$1.132$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-21}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(1\)	\(-1\)	$1$		\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots\)
2268.1.s.c	$2268$	$1$	2268.s	252.s	$6$	$2$	$1$	$1.132$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-21}) \)	None		$4$	$0$	\(1\)	\(0\)	\(-1\)	\(-1\)	$1$		\(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots\)
2268.1.s.d	$2268$	$1$	2268.s	252.s	$6$	$2$	$1$	$1.132$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-21}) \)	None		$4$	$0$	\(1\)	\(0\)	\(1\)	\(1\)	$1$		\(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots\)
2268.1.s.e	$2268$	$1$	2268.s	252.s	$6$	$8$	$4$	$1.132$	\(\Q(\zeta_{24})\)	$D_{12}$	\(\Q(\sqrt{-7}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{24}^{9}q^{2}-\zeta_{24}^{6}q^{4}-\zeta_{24}^{2}q^{7}+\cdots\)
2268.1.s.f	$2268$	$1$	2268.s	252.s	$6$	$8$	$4$	$1.132$	\(\Q(\zeta_{24})\)	$D_{12}$	\(\Q(\sqrt{-7}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{2}q^{7}+\cdots\)
2268.1.s.g	$2268$	$1$	2268.s	252.s	$6$	$8$	$4$	$1.132$	\(\Q(\zeta_{24})\)	$D_{4}$	\(\Q(\sqrt{-7}) \)	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-\zeta_{24}^{2}q^{7}+\cdots\)