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

• Label: 640.2.n
• Level: $640$
• Weight: $2$
• Character orbit: 640.n
• Rep. character: $\chi_{640}(127,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $48$
• Newform subspaces: $4$
• Sturm bound: $192$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.n (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(192\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\), \(7\)

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

\( 48 q + 16 q^{17} + 16 q^{25} - 16 q^{65} + 48 q^{73} - 112 q^{81} + 48 q^{97}+O(q^{100}) \)

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.n.a	$640$	$2$	640.n	20.e	$4$	$12$	$6$	$5.110$	12.0.\(\cdots\).1	None		✓			640.2.n.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{3}+\beta _{9}q^{5}+(-1-\beta _{3}-\beta _{5}+\cdots)q^{7}+\cdots\)
640.2.n.b	$640$	$2$	640.n	20.e	$4$	$12$	$6$	$5.110$	12.0.\(\cdots\).1	None		✓			640.2.n.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{3}q^{3}-\beta _{8}q^{5}+(-1-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
640.2.n.c	$640$	$2$	640.n	20.e	$4$	$12$	$6$	$5.110$	12.0.\(\cdots\).1	None		✓			640.2.n.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{3}q^{3}+\beta _{8}q^{5}+(1+\beta _{2}-\beta _{4}-\beta _{6}+\cdots)q^{7}+\cdots\)
640.2.n.d	$640$	$2$	640.n	20.e	$4$	$12$	$6$	$5.110$	12.0.\(\cdots\).1	None		✓			640.2.n.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{3}-\beta _{9}q^{5}+(1+\beta _{3}+\beta _{5}-\beta _{7}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(640, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)