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

• Label: 1332.1.o
• Level: $1332$
• Weight: $1$
• Character orbit: 1332.o
• Rep. character: $\chi_{1332}(253,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $2$
• 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.o (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(i)\)
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	38	2	36
Cusp forms	14	2	12
Eisenstein series	24	0	24

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	2	0

Trace form

\( 2 q - 2 q^{7} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1332.1.o.a	$1332$	$1$	1332.o	37.d	$4$	$2$	$1$	$0.665$	\(\Q(\sqrt{-1}) \)	$S_{4}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-q^{7}-iq^{11}+(1-i)q^{17}+(1-i+\cdots)q^{19}+\cdots\)

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

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