Space of modular forms of level 3332, weight 1, and Character 3332.o

• Label: 3332.1.o
• Level: $3332$
• Weight: $1$
• Character orbit: 3332.o
• Rep. character: $\chi_{3332}(67,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $7$
• Sturm bound: $504$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3332.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 476 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(504\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3332, [\chi])\).

	Total	New	Old
Modular forms	80	48	32
Cusp forms	48	32	16
Eisenstein series	32	16	16

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	32	0	0	0

Trace form

32 * q + 2 * q^2 - 6 * q^4 - 4 * q^8 - 12 * q^9 - 6 * q^16 + 4 * q^17 + 2 * q^18 + 4 * q^25 - 4 * q^26 + 10 * q^30 - 8 * q^32 - 4 * q^33 - 16 * q^36 - 24 * q^50 + 10 * q^60 + 12 * q^64 + 8 * q^66 + 4 * q^68 + 8 * q^69 + 12 * q^72 - 12 * q^81 - 10 * q^86 + 4 * q^93

Decomposition of \(S_{1}^{\mathrm{new}}(3332, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3332.1.o.a	$3332$	$1$	3332.o	476.o	$6$	$2$	$1$	$1.663$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-17}) \)	None					476.1.o.a	$4$	$0$	\(-1\)	\(-1\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+q^{6}+q^{8}+\cdots\)
3332.1.o.b	$3332$	$1$	3332.o	476.o	$6$	$2$	$1$	$1.663$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-17}) \)	None					476.1.o.a	$4$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}+q^{8}+\cdots\)
3332.1.o.c	$3332$	$1$	3332.o	476.o	$6$	$2$	$1$	$1.663$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \)	\(\Q(\sqrt{17}) \)					68.1.d.a	$8$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}-\zeta_{6}^{2}q^{9}+\cdots\)
3332.1.o.d	$3332$	$1$	3332.o	476.o	$6$	$2$	$1$	$1.663$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \)	\(\Q(\sqrt{17}) \)					68.1.d.a	$8$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}-\zeta_{6}^{2}q^{9}+\cdots\)
3332.1.o.e	$3332$	$1$	3332.o	476.o	$6$	$4$	$2$	$1.663$	\(\Q(\zeta_{12})\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-119}) \)	\(\Q(\sqrt{119}) \)		✓			3332.1.g.h	$16$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{5}q^{5}+\cdots\)
3332.1.o.f	$3332$	$1$	3332.o	476.o	$6$	$4$	$2$	$1.663$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-17}) \)	None					476.1.o.c	$8$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$3$		\(q+\zeta_{12}^{2}q^{2}+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{3}+\cdots\)
3332.1.o.g	$3332$	$1$	3332.o	476.o	$6$	$16$	$8$	$1.663$	\(\Q(\zeta_{60})\)	$D_{10}$	\(\Q(\sqrt{-119}) \)	None		✓	✓		3332.1.g.i	$16$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{60}^{4}q^{2}+(-\zeta_{60}^{11}-\zeta_{60}^{29})q^{3}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3332, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3332, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(476, [\chi])\)\(^{\oplus 2}\)