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

• Label: 320.2.d
• Level: $320$
• Weight: $2$
• Character orbit: 320.d
• Rep. character: $\chi_{320}(161,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	320.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	60	8	52
Cusp forms	36	8	28
Eisenstein series	24	0	24

Trace form

\( 8 q - 8 q^{9} - 8 q^{25} - 48 q^{33} + 48 q^{41} + 40 q^{49} + 16 q^{57} - 32 q^{73} + 8 q^{81} - 48 q^{89} + 32 q^{97}+O(q^{100}) \)

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.d.a	$320$	$2$	320.d	8.b	$2$	$4$	$4$	$2.555$	\(\Q(\zeta_{12})\)	None		✓			320.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}+\beta_1)q^{3}-\beta_1 q^{5}+(\beta_{3}-3)q^{7}+\cdots\)
320.2.d.b	$320$	$2$	320.d	8.b	$2$	$4$	$4$	$2.555$	\(\Q(\zeta_{12})\)	None		✓			320.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}+\beta_1)q^{3}+\beta_1 q^{5}+(-\beta_{3}+3)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(320, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)