Space of modular forms of level 354, weight 6, and Character 354.c

• Label: 354.6.c
• Level: $354$
• Weight: $6$
• Character orbit: 354.c
• Rep. character: $\chi_{354}(353,\cdot)$
• Character field: $\Q$
• Dimension: $100$
• Newform subspaces: $2$
• Sturm bound: $360$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	354.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 177 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(360\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(354, [\chi])\).

	Total	New	Old
Modular forms	304	100	204
Cusp forms	296	100	196
Eisenstein series	8	0	8

Trace form

\( 100 q - 26 q^{3} + 1600 q^{4} + 76 q^{7} + 102 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(354, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
354.6.c.a	$354$	$6$	354.c	177.d	$2$	$50$	$50$	$56.776$		None		$2$	$0$	\(-200\)	\(-13\)	\(0\)	\(38\)		$\mathrm{SU}(2)[C_{2}]$
354.6.c.b	$354$	$6$	354.c	177.d	$2$	$50$	$50$	$56.776$		None		$2$	$0$	\(200\)	\(-13\)	\(0\)	\(38\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{6}^{\mathrm{old}}(354, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(354, [\chi]) \cong \)