Space of modular forms of level 335, weight 1, and Character 335.d

• Label: 335.1.d
• Level: $335$
• Weight: $1$
• Character orbit: 335.d
• Rep. character: $\chi_{335}(334,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $4$
• Sturm bound: $34$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 335 = 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	335.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 335 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(34\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(335, [\chi])\).

	Total	New	Old
Modular forms	10	10	0
Cusp forms	8	8	0
Eisenstein series	2	2	0

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

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

Decomposition of \(S_{1}^{\mathrm{new}}(335, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
335.1.d.a	$335$	$1$	335.d	335.d	$2$	$1$	$1$	$0.167$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-335}) \)	None	✓	✓			335.1.d.a	$2$	$0$	\(-1\)	\(-1\)	\(1\)	\(-1\)	$1$		\(q-q^{2}-q^{3}+q^{5}+q^{6}-q^{7}+q^{8}+\cdots\)
335.1.d.b	$335$	$1$	335.d	335.d	$2$	$1$	$1$	$0.167$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-335}) \)	None	✓	✓			335.1.d.a	$2$	$0$	\(1\)	\(1\)	\(-1\)	\(1\)	$1$		\(q+q^{2}+q^{3}-q^{5}+q^{6}+q^{7}-q^{8}+\cdots\)
335.1.d.c	$335$	$1$	335.d	335.d	$2$	$3$	$3$	$0.167$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-335}) \)	None	✓	✓			335.1.d.c	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$		\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
335.1.d.d	$335$	$1$	335.d	335.d	$2$	$3$	$3$	$0.167$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-335}) \)	None	✓	✓			335.1.d.c	$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$		\(q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)