Space of modular forms of level 354, weight 2, and Character 354.g

• Label: 354.2.g
• Level: $354$
• Weight: $2$
• Character orbit: 354.g
• Rep. character: $\chi_{354}(11,\cdot)$
• Character field: $\Q(\zeta_{58})$
• Dimension: $560$
• Newform subspaces: $2$
• Sturm bound: $120$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.g (of order \(58\) and degree \(28\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 177 \)
Character field:			\(\Q(\zeta_{58})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(354, [\chi])\).

	Total	New	Old
Modular forms	1792	560	1232
Cusp forms	1568	560	1008
Eisenstein series	224	0	224

Trace form

\( 560 q + 2 q^{3} - 20 q^{4} + 4 q^{7} - 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(354, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
354.2.g.a	$354$	$2$	354.g	177.f	$58$	$280$	$10$	$2.827$		None		$2$	$0$	\(-10\)	\(1\)	\(0\)	\(2\)		$\mathrm{SU}(2)[C_{58}]$
354.2.g.b	$354$	$2$	354.g	177.f	$58$	$280$	$10$	$2.827$		None		$2$	$0$	\(10\)	\(1\)	\(0\)	\(2\)		$\mathrm{SU}(2)[C_{58}]$

Decomposition of \(S_{2}^{\mathrm{old}}(354, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(354, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(177, [\chi])\)\(^{\oplus 2}\)