Space of modular forms of level 352, weight 2, and Character 352.w

• Label: 352.2.w
• Level: $352$
• Weight: $2$
• Character orbit: 352.w
• Rep. character: $\chi_{352}(49,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $40$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.w (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 88 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(352, [\chi])\).

	Total	New	Old
Modular forms	224	56	168
Cusp forms	160	40	120
Eisenstein series	64	16	48

Trace form

\( 40 q + 10 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(352, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
352.2.w.a	$352$	$2$	352.w	88.o	$10$	$40$	$10$	$2.811$		None			✓	✓	88.2.o.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(10\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(352, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(352, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 3}\)