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

• Label: 3332.1.bc
• Level: $3332$
• Weight: $1$
• Character orbit: 3332.bc
• Rep. character: $\chi_{3332}(667,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $504$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3332.bc (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 476 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(504\)
Trace bound:			\(10\)

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	16	16	0
Eisenstein series	64	32	32

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q + 8 q^{4} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3332.1.bc.a	$3332$	$1$	3332.bc	476.ab	$12$	$4$	$1$	$1.663$	\(\Q(\zeta_{12})\)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}+\zeta_{12}^{4}+\cdots)q^{5}+\cdots\)
3332.1.bc.b	$3332$	$1$	3332.bc	476.ab	$12$	$4$	$1$	$1.663$	\(\Q(\zeta_{12})\)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}+\zeta_{12}^{4}+\cdots)q^{5}+\cdots\)
3332.1.bc.c	$3332$	$1$	3332.bc	476.ab	$12$	$4$	$1$	$1.663$	\(\Q(\zeta_{12})\)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(\zeta_{12}-\zeta_{12}^{4}+\cdots)q^{5}+\cdots\)
3332.1.bc.d	$3332$	$1$	3332.bc	476.ab	$12$	$4$	$1$	$1.663$	\(\Q(\zeta_{12})\)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(\zeta_{12}-\zeta_{12}^{4}+\cdots)q^{5}+\cdots\)