Space of modular forms of level 349, weight 2, and Character 349.b

• Label: 349.2.b
• Level: $349$
• Weight: $2$
• Character orbit: 349.b
• Rep. character: $\chi_{349}(348,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $2$
• Sturm bound: $58$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 349 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(58\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(349, [\chi])\).

	Total	New	Old
Modular forms	30	30	0
Cusp forms	28	28	0
Eisenstein series	2	2	0

Trace form

\( 28 q - 4 q^{3} - 32 q^{4} - 8 q^{5} + 28 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(349, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
349.2.b.a	$349$	$2$	349.b	349.b	$2$	$2$	$2$	$2.787$	\(\Q(\sqrt{-5}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+2q^{4}+2q^{5}+\beta q^{7}-2q^{9}+\cdots\)
349.2.b.b	$349$	$2$	349.b	349.b	$2$	$26$	$26$	$2.787$		None		$2$	$0$	\(0\)	\(-2\)	\(-12\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$