Space of modular forms of level 320, weight 2, and Character 320.f

• Label: 320.2.f
• Level: $320$
• Weight: $2$
• Character orbit: 320.f
• Rep. character: $\chi_{320}(289,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	320.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(320, [\chi])\).

	Total	New	Old
Modular forms	60	12	48
Cusp forms	36	12	24
Eisenstein series	24	0	24

Trace form

\( 12 q + 12 q^{9} + 12 q^{25} - 24 q^{41} - 12 q^{49} - 24 q^{65} - 36 q^{81} - 72 q^{89}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(320, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
320.2.f.a	$320$	$2$	320.f	40.f	$2$	$4$	$4$	$2.555$	\(\Q(i, \sqrt{5})\)	\(\Q(\sqrt{-10}) \)		✓			320.2.f.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{3}q^{5}+\beta _{2}q^{7}-3q^{9}+\beta _{1}q^{11}+\cdots\)
320.2.f.b	$320$	$2$	320.f	40.f	$2$	$8$	$8$	$2.555$	\(\Q(\zeta_{24})\)	None		✓	✓		320.2.f.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{4} q^{3}-\beta_{6} q^{5}+\beta_{2} q^{7}+3 q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(320, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(320, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)