Space of modular forms of level 3307, weight 1, and Character 3307.b

• Label: 3307.1.b
• Level: $3307$
• Weight: $1$
• Character orbit: 3307.b
• Rep. character: $\chi_{3307}(3306,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $275$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 3307 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3307.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3307 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(275\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3307, [\chi])\).

	Total	New	Old
Modular forms	5	5	0
Cusp forms	4	4	0
Eisenstein series	1	1	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + 4 q^{4} - q^{7} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3307, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3307.1.b.a	$3307$	$1$	3307.b	3307.b	$2$	$1$	$1$	$1.650$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-3307}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$		\(q+q^{4}-q^{7}+q^{9}-q^{11}+q^{16}-q^{17}+\cdots\)
3307.1.b.b	$3307$	$1$	3307.b	3307.b	$2$	$3$	$3$	$1.650$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-3307}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{4}-\beta _{1}q^{7}+q^{9}+(\beta _{1}-\beta _{2})q^{11}+\cdots\)