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

• Label: 349.2.e
• Level: $349$
• Weight: $2$
• Character orbit: 349.e
• Rep. character: $\chi_{349}(123,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $58$
• Newform subspaces: $1$
• Sturm bound: $58$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.e (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 349 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(58\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	62	62	0
Cusp forms	58	58	0
Eisenstein series	4	4	0

Trace form

\( 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9} + O(q^{10}) \)

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.e.a	$349$	$2$	349.e	349.e	$6$	$58$	$29$	$2.787$		None		$2$	$0$	\(-3\)	\(0\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$