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

• Label: 320.2.o
• Level: $320$
• Weight: $2$
• Character orbit: 320.o
• Rep. character: $\chi_{320}(223,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $6$
• Sturm bound: $96$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	320.o (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(96\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	120	24	96
Cusp forms	72	24	48
Eisenstein series	48	0	48

Trace form

\( 24 q + 24 q^{17} - 24 q^{25} - 24 q^{65} - 24 q^{73} - 120 q^{81} - 120 q^{97}+O(q^{100}) \)

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.o.a	$320$	$2$	320.o	40.k	$4$	$2$	$1$	$2.555$	\(\Q(\sqrt{-1}) \)	None		✓			320.2.o.a	$2$	$1$	\(0\)	\(-2\)	\(-2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i-1)q^{3}+(-2 i-1)q^{5}+(i-1)q^{7}+\cdots\)
320.2.o.b	$320$	$2$	320.o	40.k	$4$	$2$	$1$	$2.555$	\(\Q(\sqrt{-1}) \)	None		✓			320.2.o.a	$2$	$0$	\(0\)	\(-2\)	\(2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i-1)q^{3}+(2 i+1)q^{5}+(-i+1)q^{7}+\cdots\)
320.2.o.c	$320$	$2$	320.o	40.k	$4$	$2$	$1$	$2.555$	\(\Q(\sqrt{-1}) \)	None		✓			320.2.o.a	$2$	$0$	\(0\)	\(2\)	\(-2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i+1)q^{3}+(-2 i-1)q^{5}+(-i+1)q^{7}+\cdots\)
320.2.o.d	$320$	$2$	320.o	40.k	$4$	$2$	$1$	$2.555$	\(\Q(\sqrt{-1}) \)	None		✓			320.2.o.a	$2$	$0$	\(0\)	\(2\)	\(2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i+1)q^{3}+(2 i+1)q^{5}+(i-1)q^{7}+\cdots\)
320.2.o.e	$320$	$2$	320.o	40.k	$4$	$8$	$4$	$2.555$	8.0.49787136.1	None		✓			320.2.o.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta _{2}-\beta _{7})q^{3}+\beta _{7}q^{5}-\beta _{6}q^{7}+\cdots\)
320.2.o.f	$320$	$2$	320.o	40.k	$4$	$8$	$4$	$2.555$	8.0.49787136.1	None		✓			320.2.o.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta _{2}-\beta _{7})q^{3}-\beta _{7}q^{5}+\beta _{6}q^{7}+\cdots\)

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

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