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

• Label: 2268.1.bd
• Level: $2268$
• Weight: $1$
• Character orbit: 2268.bd
• Rep. character: $\chi_{2268}(1405,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $432$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2268.bd (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(432\)
Trace bound:			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	82	4	78
Cusp forms	10	4	6
Eisenstein series	72	0	72

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

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

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2268.1.bd.a	$2268$	$1$	2268.bd	63.t	$6$	$2$	$1$	$1.132$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None					252.1.z.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-q^{7}+(-1+\zeta_{6}^{2})q^{13}+(-1+\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
2268.1.bd.b	$2268$	$1$	2268.bd	63.t	$6$	$2$	$1$	$1.132$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None					756.1.z.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$		\(q+\zeta_{6}q^{7}+(1-\zeta_{6}^{2})q^{19}-\zeta_{6}q^{25}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(2268, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 3}\)