Space of modular forms of level 354, weight 3, and Character 354.h

• Label: 354.3.h
• Level: $354$
• Weight: $3$
• Character orbit: 354.h
• Rep. character: $\chi_{354}(5,\cdot)$
• Character field: $\Q(\zeta_{58})$
• Dimension: $1120$
• Newform subspaces: $1$
• Sturm bound: $180$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	354.h (of order \(58\) and degree \(28\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 177 \)
Character field:			\(\Q(\zeta_{58})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(180\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(354, [\chi])\).

	Total	New	Old
Modular forms	3472	1120	2352
Cusp forms	3248	1120	2128
Eisenstein series	224	0	224

Trace form

\( 1120 q + 80 q^{4} - 8 q^{6} - 8 q^{7} + 24 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(354, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
354.3.h.a	$354$	$3$	354.h	177.h	$58$	$1120$	$40$	$9.646$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{58}]$

Decomposition of \(S_{3}^{\mathrm{old}}(354, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(354, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(177, [\chi])\)\(^{\oplus 2}\)