Space of modular forms of level 354, weight 7, and Character 354.d

• Label: 354.7.d
• Level: $354$
• Weight: $7$
• Character orbit: 354.d
• Rep. character: $\chi_{354}(235,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $1$
• Sturm bound: $420$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	354.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 59 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(420\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(354, [\chi])\).

	Total	New	Old
Modular forms	364	60	304
Cusp forms	356	60	296
Eisenstein series	8	0	8

Trace form

\( 60 q - 1920 q^{4} + 408 q^{7} + 14580 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(354, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
354.7.d.a	$354$	$7$	354.d	59.b	$2$	$60$	$60$	$81.439$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(408\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{7}^{\mathrm{old}}(354, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(354, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(118, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(177, [\chi])\)\(^{\oplus 2}\)