Space of modular forms of level 336, weight 1, and Character 336.o

• Label: 336.1.o
• Level: $336$
• Weight: $1$
• Character orbit: 336.o
• Rep. character: $\chi_{336}(335,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $64$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	336.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 84 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(64\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(336, [\chi])\).

	Total	New	Old
Modular forms	14	2	12
Cusp forms	2	2	0
Eisenstein series	12	0	12

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

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

Decomposition of \(S_{1}^{\mathrm{new}}(336, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
336.1.o.a	$336$	$1$	336.o	84.h	$2$	$1$	$1$	$0.168$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-21}) \)	\(\Q(\sqrt{7}) \)	✓	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)	$1$		\(q-q^{3}+q^{7}+q^{9}+2q^{19}-q^{21}-q^{25}+\cdots\)
336.1.o.b	$336$	$1$	336.o	84.h	$2$	$1$	$1$	$0.168$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-21}) \)	\(\Q(\sqrt{7}) \)	✓	$4$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)	$1$		\(q+q^{3}-q^{7}+q^{9}-2q^{19}-q^{21}-q^{25}+\cdots\)