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

• Label: 2268.1.h
• Level: $2268$
• Weight: $1$
• Character orbit: 2268.h
• Rep. character: $\chi_{2268}(2267,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $432$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2268.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 84 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(432\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	52	16	36
Cusp forms	28	8	20
Eisenstein series	24	8	16

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

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

Trace form

\( 8 q + O(q^{10}) \)

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.h.a	$2268$	$1$	2268.h	84.h	$2$	$8$	$8$	$1.132$	\(\Q(\zeta_{24})\)	$D_{12}$	\(\Q(\sqrt{-7}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+\zeta_{24}^{6}q^{7}-\zeta_{24}^{3}q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2268, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2268, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)