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

• Label: 640.2.j
• Level: $640$
• Weight: $2$
• Character orbit: 640.j
• Rep. character: $\chi_{640}(543,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $40$
• Newform subspaces: $4$
• Sturm bound: $192$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(192\)
Trace bound:			\(7\)
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	56	168
Cusp forms	160	40	120
Eisenstein series	64	16	48

Trace form

\( 40 q + 4 q^{5} - 24 q^{9} + O(q^{10}) \)

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.j.a	$640$	$2$	640.j	80.j	$4$	$2$	$1$	$5.110$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-2iq^{3}+(-1-2i)q^{5}+(-3-3i)q^{7}+\cdots\)
640.2.j.b	$640$	$2$	640.j	80.j	$4$	$2$	$1$	$5.110$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+2iq^{3}+(-1-2i)q^{5}+(3+3i)q^{7}+\cdots\)
640.2.j.c	$640$	$2$	640.j	80.j	$4$	$18$	$9$	$5.110$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(-2\)	$2^{13}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{12}q^{3}-\beta _{6}q^{5}-\beta _{11}q^{7}+(-1+\cdots)q^{9}+\cdots\)
640.2.j.d	$640$	$2$	640.j	80.j	$4$	$18$	$9$	$5.110$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(2\)	$2^{13}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{12}q^{3}+\beta _{4}q^{5}-\beta _{10}q^{7}+(-1+\cdots)q^{9}+\cdots\)

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

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