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

• Label: 1332.1.cz
• Level: $1332$
• Weight: $1$
• Character orbit: 1332.cz
• Rep. character: $\chi_{1332}(127,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $6$
• 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.cz (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 148 \)
Character field:			\(\Q(\zeta_{18})\)
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	72	18	54
Cusp forms	24	6	18
Eisenstein series	48	12	36

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q + 3 q^{5} + 3 q^{8} + O(q^{10}) \)

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.cz.a	$1332$	$1$	1332.cz	148.p	$18$	$6$	$1$	$0.665$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-1}) \)	None			✓	✓	148.1.p.a	$4$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$		\(q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+(-\zeta_{18}^{6}+\zeta_{18}^{7}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1332, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1332, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(444, [\chi])\)\(^{\oplus 2}\)