Space of modular forms of level 3364, weight 1, and Character 3364.b

• Label: 3364.1.b
• Level: $3364$
• Weight: $1$
• Character orbit: 3364.b
• Rep. character: $\chi_{3364}(1683,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $435$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 3364 = 2^{2} \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3364.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(435\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3364, [\chi])\).

	Total	New	Old
Modular forms	38	35	3
Cusp forms	8	8	0
Eisenstein series	30	27	3

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q + 4 q^{4} + 2 q^{6} + 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3364, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3364.1.b.a	$3364$	$1$	3364.b	4.b	$2$	$2$	$2$	$1.679$	\(\Q(\sqrt{-1}) \)	$D_{3}$	\(\Q(\sqrt{-29}) \)	None		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-iq^{2}+iq^{3}-q^{4}+q^{5}+q^{6}+iq^{8}+\cdots\)
3364.1.b.b	$3364$	$1$	3364.b	4.b	$2$	$3$	$3$	$1.679$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-1}) \)	None	✓	$2$	$0$	\(-3\)	\(0\)	\(-1\)	\(0\)	$1$		\(q-q^{2}+q^{4}-\beta _{1}q^{5}-q^{8}+q^{9}+\beta _{1}q^{10}+\cdots\)
3364.1.b.c	$3364$	$1$	3364.b	4.b	$2$	$3$	$3$	$1.679$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-1}) \)	None	✓	$2$	$0$	\(3\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+q^{2}+q^{4}-\beta _{1}q^{5}+q^{8}+q^{9}-\beta _{1}q^{10}+\cdots\)