Space of modular forms of level 1332, weight 1, and Character 1332.bj

• Label: 1332.1.bj
• Level: $1332$
• Weight: $1$
• Character orbit: 1332.bj
• Rep. character: $\chi_{1332}(307,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $228$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1332 = 2^{2} \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1332.bj (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 148 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(228\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1332, [\chi])\).

	Total	New	Old
Modular forms	20	8	12
Cusp forms	4	4	0
Eisenstein series	16	4	12

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

\( 4 q + 2 q^{4} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1332, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1332.1.bj.a	$1332$	$1$	1332.bj	148.j	$6$	$4$	$2$	$0.665$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	1332.1.bj.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)