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

• Label: 640.2.c
• Level: $640$
• Weight: $2$
• Character orbit: 640.c
• Rep. character: $\chi_{640}(129,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $192$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(192\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(11\), \(29\)

Dimensions

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

	Total	New	Old
Modular forms	112	24	88
Cusp forms	80	24	56
Eisenstein series	32	0	32

Trace form

\( 24 q - 24 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
640.2.c.a	$640$	$2$	640.c	5.b	$2$	$6$	$6$	$5.110$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(\beta _{2}+\beta _{5})q^{5}+(\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
640.2.c.b	$640$	$2$	640.c	5.b	$2$	$6$	$6$	$5.110$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
640.2.c.c	$640$	$2$	640.c	5.b	$2$	$6$	$6$	$5.110$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{5})q^{5}+(-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
640.2.c.d	$640$	$2$	640.c	5.b	$2$	$6$	$6$	$5.110$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)

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

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