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

• Label: 3332.1.cc
• Level: $3332$
• Weight: $1$
• Character orbit: 3332.cc
• Rep. character: $\chi_{3332}(135,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $48$
• Newform subspaces: $3$
• Sturm bound: $504$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3332.cc (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3332 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(504\)
Trace bound:			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	96	96	0
Cusp forms	48	48	0
Eisenstein series	48	48	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	48	0	0	0

Trace form

\( 48 q + 4 q^{4} + 4 q^{9} + O(q^{10}) \)

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.cc.a	$3332$	$1$	3332.cc	3332.bc	$42$	$12$	$1$	$1.663$	\(\Q(\zeta_{21})\)	$D_{21}$	\(\Q(\sqrt{-17}) \)	None		$4$	$0$	\(1\)	\(-13\)	\(0\)	\(2\)	$1$		\(q-\zeta_{42}^{17}q^{2}+(-1+\zeta_{42}^{11})q^{3}-\zeta_{42}^{13}q^{4}+\cdots\)
3332.1.cc.b	$3332$	$1$	3332.cc	3332.bc	$42$	$12$	$1$	$1.663$	\(\Q(\zeta_{21})\)	$D_{21}$	\(\Q(\sqrt{-17}) \)	None		$4$	$0$	\(1\)	\(13\)	\(0\)	\(-2\)	$1$		\(q-\zeta_{42}^{17}q^{2}+(1-\zeta_{42}^{11})q^{3}-\zeta_{42}^{13}q^{4}+\cdots\)
3332.1.cc.c	$3332$	$1$	3332.cc	3332.bc	$42$	$24$	$2$	$1.663$	\(\Q(\zeta_{84})\)	$D_{42}$	\(\Q(\sqrt{-17}) \)	None		$8$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{84}^{40}q^{2}+(\zeta_{84}^{21}-\zeta_{84}^{37})q^{3}+\cdots\)