Space of modular forms of level 338, weight 2, and Character 338.b

• Label: 338.2.b
• Level: $338$
• Weight: $2$
• Character orbit: 338.b
• Rep. character: $\chi_{338}(337,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $4$
• Sturm bound: $91$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	338.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(91\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(338, [\chi])\).

	Total	New	Old
Modular forms	60	12	48
Cusp forms	32	12	20
Eisenstein series	28	0	28

Trace form

\( 12 q + 2 q^{3} - 12 q^{4} + 18 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(338, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
338.2.b.a	$338$	$2$	338.b	13.b	$2$	$2$	$2$	$2.699$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-3q^{3}-q^{4}-iq^{5}-3iq^{6}+\cdots\)
338.2.b.b	$338$	$2$	338.b	13.b	$2$	$2$	$2$	$2.699$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}-iq^{5}-4iq^{7}-iq^{8}+\cdots\)
338.2.b.c	$338$	$2$	338.b	13.b	$2$	$2$	$2$	$2.699$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{3}-q^{4}+3iq^{5}+iq^{6}+\cdots\)
338.2.b.d	$338$	$2$	338.b	13.b	$2$	$6$	$6$	$2.699$	6.0.153664.1	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+(1+\beta _{2}-\beta _{4})q^{3}-q^{4}-2\beta _{1}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(338, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(338, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)