Space of modular forms of level 640, weight 2, and Character 640.o

• Label: 640.2.o
• Level: $640$
• Weight: $2$
• Character orbit: 640.o
• Rep. character: $\chi_{640}(63,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $48$
• Newform subspaces: $11$
• Sturm bound: $192$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.o (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(192\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(640, [\chi])\).

	Total	New	Old
Modular forms	224	48	176
Cusp forms	160	48	112
Eisenstein series	64	0	64

Trace form

\( 48 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(640, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
640.2.o.a	$640$	$2$	640.o	40.k	$4$	$2$	$1$	$5.110$	\(\Q(\sqrt{-1}) \)	None		✓			640.2.o.a	$2$	$1$	\(0\)	\(-4\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2+2i)q^{3}+(-2+i)q^{5}+(-2+\cdots)q^{7}+\cdots\)
640.2.o.b	$640$	$2$	640.o	40.k	$4$	$2$	$1$	$5.110$	\(\Q(\sqrt{-1}) \)	None		✓			640.2.o.a	$2$	$0$	\(0\)	\(-4\)	\(4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2+2i)q^{3}+(2-i)q^{5}+(2-2i)q^{7}+\cdots\)
640.2.o.c	$640$	$2$	640.o	40.k	$4$	$2$	$1$	$5.110$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		✓			640.2.o.c	$4$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-2+i)q^{5}+3iq^{9}+(-5-5i)q^{13}+\cdots\)
640.2.o.d	$640$	$2$	640.o	40.k	$4$	$2$	$1$	$5.110$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		✓			640.2.o.d	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-2-i)q^{5}+3iq^{9}+(1+i)q^{13}+\cdots\)
640.2.o.e	$640$	$2$	640.o	40.k	$4$	$2$	$1$	$5.110$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		✓			640.2.o.d	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(2+i)q^{5}+3iq^{9}+(-1-i)q^{13}+\cdots\)
640.2.o.f	$640$	$2$	640.o	40.k	$4$	$2$	$1$	$5.110$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		✓			640.2.o.c	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(2-i)q^{5}+3iq^{9}+(5+5i)q^{13}+\cdots\)
640.2.o.g	$640$	$2$	640.o	40.k	$4$	$2$	$1$	$5.110$	\(\Q(\sqrt{-1}) \)	None		✓			640.2.o.a	$2$	$0$	\(0\)	\(4\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2-2i)q^{3}+(-2+i)q^{5}+(2-2i)q^{7}+\cdots\)
640.2.o.h	$640$	$2$	640.o	40.k	$4$	$2$	$1$	$5.110$	\(\Q(\sqrt{-1}) \)	None		✓			640.2.o.a	$2$	$0$	\(0\)	\(4\)	\(4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2-2i)q^{3}+(2-i)q^{5}+(-2+2i)q^{7}+\cdots\)
640.2.o.i	$640$	$2$	640.o	40.k	$4$	$8$	$4$	$5.110$	8.0.40960000.1	None		✓			640.2.o.i	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{1}q^{3}-\beta _{5}q^{5}+\beta _{2}q^{7}+\beta _{3}q^{9}+\cdots\)
640.2.o.j	$640$	$2$	640.o	40.k	$4$	$12$	$6$	$5.110$	12.0.\(\cdots\).1	None		✓			640.2.o.j	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{3}+\beta _{3}q^{5}+\beta _{1}q^{7}+(\beta _{5}+\beta _{7}+\cdots)q^{9}+\cdots\)
640.2.o.k	$640$	$2$	640.o	40.k	$4$	$12$	$6$	$5.110$	12.0.\(\cdots\).1	None		✓			640.2.o.j	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{3}-\beta _{3}q^{5}-\beta _{1}q^{7}+(\beta _{5}+\beta _{7}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(640, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(640, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)